==========Source and Output for LSODE Demonstration Program=====================
c-----------------------------------------------------------------------
c Demonstration program for the SLSODE package.
c This is the version of 12 June 2001.
c
c This version is in single precision.
c
c The package is used to solve two simple problems,
c one with a full Jacobian, the other with a banded Jacobian,
c with all 8 of the appropriate values of mf in each case.
c If the errors are too large, or other difficulty occurs,
c a warning message is printed. All output is on unit lout = 6.
c-----------------------------------------------------------------------
external f1, jac1, f2, jac2
integer i, iopar, iopt, iout, istate, itask, itol, iwork,
1 leniw, lenrw, liw, lout, lrw, mband, meth, mf, miter,
2 ml, mu, neq, nerr, nfe, nfea, nje, nout, nqu, nst
real atol, dtout, er, erm, ero, hu, rtol, rwork, t,
1 tout, tout1, y
dimension y(25), rwork(697), iwork(45)
data lout/6/, tout1/1.39283880203e0/, dtout/2.214773875e0/
c
nerr = 0
itol = 1
rtol = 0.0e0
atol = 1.0e-6
lrw = 697
liw = 45
iopt = 0
c
c First problem
c
neq = 2
nout = 4
write (lout,110) neq,itol,rtol,atol
110 format(/' Demonstration program for SLSODE package'///
1 ' Problem 1: Van der Pol oscillator:'/
2 ' xdotdot - 3*(1 - x**2)*xdot + x = 0, ',
3 ' x(0) = 2, xdot(0) = 0'/
4 ' neq =',i2/
5 ' itol =',i3,' rtol =',e10.1,' atol =',e10.1//)
c
do 195 meth = 1,2
do 190 miter = 0,3
mf = 10*meth + miter
write (lout,120) mf
120 format(///' Solution with mf =',i3//
1 5x,'t x xdot nq h'//)
t = 0.0e0
y(1) = 2.0e0
y(2) = 0.0e0
itask = 1
istate = 1
tout = tout1
ero = 0.0e0
do 170 iout = 1,nout
call slsode(f1,neq,y,t,tout,itol,rtol,atol,itask,istate,
1 iopt,rwork,lrw,iwork,liw,jac1,mf)
hu = rwork(11)
nqu = iwork(14)
write (lout,140) t,y(1),y(2),nqu,hu
140 format(e15.5,e16.5,e14.3,i5,e14.3)
if (istate .lt. 0) go to 175
iopar = iout - 2*(iout/2)
if (iopar .ne. 0) go to 170
er = abs(y(1))/atol
ero = max(ero,er)
if (er .gt. 1000.0e0) then
write (lout,150)
150 format(//' Warning: error exceeds 1000 * tolerance'//)
nerr = nerr + 1
endif
170 tout = tout + dtout
175 continue
if (istate .lt. 0) nerr = nerr + 1
nst = iwork(11)
nfe = iwork(12)
nje = iwork(13)
lenrw = iwork(17)
leniw = iwork(18)
nfea = nfe
if (miter .eq. 2) nfea = nfe - neq*nje
if (miter .eq. 3) nfea = nfe - nje
write (lout,180) lenrw,leniw,nst,nfe,nfea,nje,ero
180 format(//' Final statistics for this run:'/
1 ' rwork size =',i4,' iwork size =',i4/
2 ' number of steps =',i5/
3 ' number of f-s =',i5/
4 ' (excluding J-s) =',i5/
5 ' number of J-s =',i5/
6 ' error overrun =',e10.2)
190 continue
195 continue
c
c Second problem
c
neq = 25
ml = 5
mu = 0
iwork(1) = ml
iwork(2) = mu
mband = ml + mu + 1
nout = 5
write (lout,210) neq,ml,mu,itol,rtol,atol
210 format(///70('-')///
1 ' Problem 2: ydot = A * y , where',
2 ' A is a banded lower triangular matrix'/
3 12x, 'derived from 2-D advection PDE'/
4 ' neq =',i3,' ml =',i2,' mu =',i2/
5 ' itol =',i3,' rtol =',e10.1,' atol =',e10.1//)
do 295 meth = 1,2
do 290 miter = 0,5
if (miter .eq. 1 .or. miter .eq. 2) go to 290
mf = 10*meth + miter
write (lout,220) mf
220 format(///' Solution with mf =',i3//
1 5x,'t max.err. nq h'//)
t = 0.0e0
do 230 i = 2,neq
230 y(i) = 0.0e0
y(1) = 1.0e0
itask = 1
istate = 1
tout = 0.01e0
ero = 0.0e0
do 270 iout = 1,nout
call slsode(f2,neq,y,t,tout,itol,rtol,atol,itask,istate,
1 iopt,rwork,lrw,iwork,liw,jac2,mf)
call edit2(y,t,erm)
hu = rwork(11)
nqu = iwork(14)
write (lout,240) t,erm,nqu,hu
240 format(e15.5,e14.3,i5,e14.3)
if (istate .lt. 0) go to 275
er = erm/atol
ero = max(ero,er)
if (er .gt. 1000.0e0) then
write (lout,150)
nerr = nerr + 1
endif
270 tout = tout*10.0e0
275 continue
if (istate .lt. 0) nerr = nerr + 1
nst = iwork(11)
nfe = iwork(12)
nje = iwork(13)
lenrw = iwork(17)
leniw = iwork(18)
nfea = nfe
if (miter .eq. 5) nfea = nfe - mband*nje
if (miter .eq. 3) nfea = nfe - nje
write (lout,180) lenrw,leniw,nst,nfe,nfea,nje,ero
290 continue
295 continue
write (lout,300) nerr
300 format(////' Number of errors encountered =',i3)
stop
end
subroutine f1 (neq, t, y, ydot)
integer neq
real t, y, ydot
dimension y(neq), ydot(neq)
ydot(1) = y(2)
ydot(2) = 3.0e0*(1.0e0 - y(1)*y(1))*y(2) - y(1)
return
end
subroutine jac1 (neq, t, y, ml, mu, pd, nrowpd)
integer neq, ml, mu, nrowpd
real t, y, pd
dimension y(neq), pd(nrowpd,neq)
pd(1,1) = 0.0e0
pd(1,2) = 1.0e0
pd(2,1) = -6.0e0*y(1)*y(2) - 1.0e0
pd(2,2) = 3.0e0*(1.0e0 - y(1)*y(1))
return
end
subroutine f2 (neq, t, y, ydot)
integer neq, i, j, k, ng
real t, y, ydot, alph1, alph2, d
dimension y(neq), ydot(neq)
data alph1/1.0e0/, alph2/1.0e0/, ng/5/
do 10 j = 1,ng
do 10 i = 1,ng
k = i + (j - 1)*ng
d = -2.0e0*y(k)
if (i .ne. 1) d = d + y(k-1)*alph1
if (j .ne. 1) d = d + y(k-ng)*alph2
10 ydot(k) = d
return
end
subroutine jac2 (neq, t, y, ml, mu, pd, nrowpd)
integer neq, ml, mu, nrowpd, j, mband, mu1, mu2, ng
real t, y, pd, alph1, alph2
dimension y(neq), pd(nrowpd,neq)
data alph1/1.0e0/, alph2/1.0e0/, ng/5/
mband = ml + mu + 1
mu1 = mu + 1
mu2 = mu + 2
do 10 j = 1,neq
pd(mu1,j) = -2.0e0
pd(mu2,j) = alph1
10 pd(mband,j) = alph2
do 20 j = ng,neq,ng
20 pd(mu2,j) = 0.0e0
return
end
subroutine edit2 (y, t, erm)
integer i, j, k, ng
real y, t, erm, alph1, alph2, a1, a2, er, ex, yt
dimension y(25)
data alph1/1.0e0/, alph2/1.0e0/, ng/5/
erm = 0.0e0
if (t .eq. 0.0e0) return
ex = 0.0e0
if (t .le. 30.0e0) ex = exp(-2.0e0*t)
a2 = 1.0e0
do 60 j = 1,ng
a1 = 1.0e0
do 50 i = 1,ng
k = i + (j - 1)*ng
yt = t**(i+j-2)*ex*a1*a2
er = abs(y(k)-yt)
erm = max(erm,er)
a1 = a1*alph1/i
50 continue
a2 = a2*alph2/j
60 continue
return
end
................................................................................
Demonstration program for DLSODE package
Problem 1: Van der Pol oscillator:
xdotdot - 3*(1 - x**2)*xdot + x = 0, x(0) = 2, xdot(0) = 0
neq = 2
itol = 1 rtol = 0.0E+00 atol = 0.1E-05
Solution with mf = 10
t x xdot nq h
0.13928E+01 0.16801E+01 -0.291E+00 3 0.123E+00
0.36076E+01 -0.77986E-04 -0.317E+01 5 0.217E-01
0.58224E+01 -0.16801E+01 0.291E+00 3 0.475E-01
0.80372E+01 0.11669E-03 0.317E+01 5 0.234E-01
Final statistics for this run:
rwork size = 52 iwork size = 20
number of steps = 297
number of f-s = 352
(excluding J-s) = 352
number of J-s = 0
error overrun = 0.12E+03
Solution with mf = 11
t x xdot nq h
0.13928E+01 0.16801E+01 -0.291E+00 5 0.121E+00
0.36076E+01 -0.17732E-04 -0.317E+01 5 0.187E-01
0.58224E+01 -0.16801E+01 0.291E+00 6 0.963E-01
0.80372E+01 0.25894E-04 0.317E+01 5 0.190E-01
Final statistics for this run:
rwork size = 58 iwork size = 22
number of steps = 203
number of f-s = 281
(excluding J-s) = 281
number of J-s = 29
error overrun = 0.26E+02
Solution with mf = 12
t x xdot nq h
0.13928E+01 0.16801E+01 -0.291E+00 5 0.121E+00
0.36076E+01 -0.17732E-04 -0.317E+01 5 0.187E-01
0.58224E+01 -0.16801E+01 0.291E+00 6 0.963E-01
0.80372E+01 0.25894E-04 0.317E+01 5 0.190E-01
Final statistics for this run:
rwork size = 58 iwork size = 22
number of steps = 203
number of f-s = 339
(excluding J-s) = 281
number of J-s = 29
error overrun = 0.26E+02
Solution with mf = 13
t x xdot nq h
0.13928E+01 0.16801E+01 -0.291E+00 5 0.739E-01
0.36076E+01 0.34401E-04 -0.317E+01 6 0.260E-01
0.58224E+01 -0.16801E+01 0.291E+00 4 0.133E+00
0.80372E+01 -0.59053E-04 0.317E+01 5 0.205E-01
Final statistics for this run:
rwork size = 56 iwork size = 20
number of steps = 198
number of f-s = 315
(excluding J-s) = 289
number of J-s = 26
error overrun = 0.59E+02
Solution with mf = 20
t x xdot nq h
0.13928E+01 0.16801E+01 -0.291E+00 5 0.549E-01
0.36076E+01 -0.56579E-04 -0.317E+01 5 0.143E-01
0.58224E+01 -0.16801E+01 0.291E+00 4 0.583E-01
0.80372E+01 0.10387E-03 0.317E+01 5 0.149E-01
Final statistics for this run:
rwork size = 38 iwork size = 20
number of steps = 289
number of f-s = 321
(excluding J-s) = 321
number of J-s = 0
error overrun = 0.10E+03
Solution with mf = 21
t x xdot nq h
0.13928E+01 0.16801E+01 -0.291E+00 5 0.676E-01
0.36076E+01 -0.48977E-04 -0.317E+01 5 0.141E-01
0.58224E+01 -0.16801E+01 0.291E+00 5 0.126E+00
0.80372E+01 0.96867E-04 0.317E+01 5 0.142E-01
Final statistics for this run:
rwork size = 44 iwork size = 22
number of steps = 262
number of f-s = 345
(excluding J-s) = 345
number of J-s = 30
error overrun = 0.97E+02
Solution with mf = 22
t x xdot nq h
0.13928E+01 0.16801E+01 -0.291E+00 5 0.676E-01
0.36076E+01 -0.48977E-04 -0.317E+01 5 0.141E-01
0.58224E+01 -0.16801E+01 0.291E+00 5 0.126E+00
0.80372E+01 0.96867E-04 0.317E+01 5 0.142E-01
Final statistics for this run:
rwork size = 44 iwork size = 22
number of steps = 262
number of f-s = 405
(excluding J-s) = 345
number of J-s = 30
error overrun = 0.97E+02
Solution with mf = 23
t x xdot nq h
0.13928E+01 0.16801E+01 -0.291E+00 5 0.709E-01
0.36076E+01 -0.46705E-04 -0.317E+01 5 0.139E-01
0.58224E+01 -0.16801E+01 0.291E+00 3 0.719E-01
0.80372E+01 0.54700E-04 0.317E+01 5 0.154E-01
Final statistics for this run:
rwork size = 42 iwork size = 20
number of steps = 271
number of f-s = 414
(excluding J-s) = 383
number of J-s = 31
error overrun = 0.55E+02
----------------------------------------------------------------------
Problem 2: ydot = A * y , where A is a banded lower triangular matrix
derived from 2-D advection PDE
neq = 25 ml = 5 mu = 0
itol = 1 rtol = 0.0E+00 atol = 0.1E-05
Solution with mf = 10
t max.err. nq h
0.10000E-01 0.556E-06 2 0.766E-02
0.10000E+00 0.655E-05 3 0.249E-01
0.10000E+01 0.274E-05 4 0.520E-01
0.10000E+02 0.114E-05 3 0.117E+00
0.10000E+03 0.221E-05 2 0.262E+00
Final statistics for this run:
rwork size = 420 iwork size = 20
number of steps = 524
number of f-s = 552
(excluding J-s) = 552
number of J-s = 0
error overrun = 0.65E+01
Solution with mf = 13
t max.err. nq h
0.10000E-01 0.839E-06 2 0.949E-02
0.10000E+00 0.208E-05 3 0.250E-01
0.10000E+01 0.127E-03 3 0.168E-01
0.10000E+02 0.113E-04 3 0.385E+00
0.10000E+03 0.145E-05 2 0.149E+02
Final statistics for this run:
rwork size = 447 iwork size = 20
number of steps = 129
number of f-s = 235
(excluding J-s) = 201
number of J-s = 34
error overrun = 0.13E+03
Solution with mf = 14
t max.err. nq h
0.10000E-01 0.877E-06 2 0.965E-02
0.10000E+00 0.206E-05 3 0.250E-01
0.10000E+01 0.126E-05 5 0.935E-01
0.10000E+02 0.311E-06 6 0.442E+00
0.10000E+03 0.159E-07 2 0.291E+02
Final statistics for this run:
rwork size = 697 iwork size = 45
number of steps = 92
number of f-s = 113
(excluding J-s) = 113
number of J-s = 18
error overrun = 0.21E+01
Solution with mf = 15
t max.err. nq h
0.10000E-01 0.877E-06 2 0.965E-02
0.10000E+00 0.206E-05 3 0.250E-01
0.10000E+01 0.126E-05 5 0.935E-01
0.10000E+02 0.311E-06 6 0.442E+00
0.10000E+03 0.160E-07 2 0.291E+02
Final statistics for this run:
rwork size = 697 iwork size = 45
number of steps = 92
number of f-s = 221
(excluding J-s) = 113
number of J-s = 18
error overrun = 0.21E+01
Solution with mf = 20
t max.err. nq h
0.10000E-01 0.465E-06 2 0.483E-02
0.10000E+00 0.131E-05 3 0.148E-01
0.10000E+01 0.427E-05 5 0.635E-01
0.10000E+02 0.192E-05 4 0.351E+00
0.10000E+03 0.929E-07 1 0.455E+00
Final statistics for this run:
rwork size = 245 iwork size = 20
number of steps = 330
number of f-s = 530
(excluding J-s) = 530
number of J-s = 0
error overrun = 0.43E+01
Solution with mf = 23
t max.err. nq h
0.10000E-01 0.101E-05 2 0.598E-02
0.10000E+00 0.446E-06 3 0.146E-01
0.10000E+01 0.153E-05 5 0.738E-01
0.10000E+02 0.578E-06 4 0.324E+00
0.10000E+03 0.908E-08 1 0.992E+02
Final statistics for this run:
rwork size = 272 iwork size = 20
number of steps = 180
number of f-s = 325
(excluding J-s) = 274
number of J-s = 51
error overrun = 0.15E+01
Solution with mf = 24
t max.err. nq h
0.10000E-01 0.104E-05 2 0.608E-02
0.10000E+00 0.463E-06 3 0.146E-01
0.10000E+01 0.247E-05 5 0.666E-01
0.10000E+02 0.828E-06 5 0.391E+00
0.10000E+03 0.384E-09 1 0.108E+03
Final statistics for this run:
rwork size = 522 iwork size = 45
number of steps = 118
number of f-s = 136
(excluding J-s) = 136
number of J-s = 18
error overrun = 0.25E+01
Solution with mf = 25
t max.err. nq h
0.10000E-01 0.104E-05 2 0.608E-02
0.10000E+00 0.463E-06 3 0.146E-01
0.10000E+01 0.247E-05 5 0.666E-01
0.10000E+02 0.828E-06 5 0.391E+00
0.10000E+03 0.384E-09 1 0.108E+03
Final statistics for this run:
rwork size = 522 iwork size = 45
number of steps = 118
number of f-s = 244
(excluding J-s) = 136
number of J-s = 18
error overrun = 0.25E+01
Number of errors encountered = 0
==========Source and Output for LSODES Demonstration Program====================
c-----------------------------------------------------------------------
c Demonstration program for the SLSODES package.
c This is the version of 12 June 2001.
c
c This version is in single precision.
c
c The package is used for each of the relevant values of mf to solve
c the problem ydot = A * y, where A is the 9 by 9 sparse matrix
c
c -4 1 1
c 1 -4 1 1
c 1 -4 1
c -4 1 1
c A = 1 -4 1 1
c 1 -4 1
c -4 1
c 1 -4 1
c 1 -4
c
c The initial conditions are y(0) = (1, 2, 3, ..., 9).
c Output is printed at t = 1, 2, and 3.
c Each case is solved first with nominal (large) values of lrw and liw,
c and then with values given by lenrw and leniw (optional outputs)
c on the first run, as a check on these computed work array lengths.
c If the errors are too large, or other difficulty occurs,
c a warning message is printed.
c All output is on unit lout, which is data-loaded to 6 below.
c-----------------------------------------------------------------------
external fdem, jdem
integer i, ia, igrid, iopt, iout, irun, istate, itask, itol,
1 iwork, j, ja, k, l, leniw, lenrw, liw, lout, lrw,
2 m, meth, mf, miter, moss, neq, nerr, nfe, nfea,
3 ngp, nje, nlu, nnz, nout, nqu, nst, nzl, nzu
real atol, erm, ero, hu, rtol, rwork, t, tout, y
dimension y(9), ia(10), ja(50), iwork(90), rwork(1000)
equivalence (ia(1),iwork(31)), (ja(1),iwork(41))
data lout/6/
c
c Write heading and set fixed parameters.
write(lout,10)
10 format(/'Demonstration problem for the SLSODES package'//)
nerr = 0
igrid = 3
neq = igrid**2
t = 0.0e0
itol = 1
rtol = 0.0e0
atol = 1.0e-5
itask = 1
iopt = 0
do 20 i = 1,neq
20 y(i) = i
ia(1) = 1
k = 1
do 60 m = 1,igrid
do 50 l = 1,igrid
j = l + (m - 1)*igrid
if (m .gt. 1) then
ja(k) = j - igrid
k = k + 1
endif
30 if (l .gt. 1) then
ja(k) = j - 1
k = k + 1
endif
35 ja(k) = j
k = k + 1
if (l .lt. igrid) then
ja(k) = j + 1
k = k + 1
endif
40 ia(j+1) = k
50 continue
60 continue
write (lout,80)neq,t,rtol,atol,(y(i),i=1,neq)
80 format(' neq =',i4,5x,'t0 =',f4.1,5x,'rtol =',e12.3,5x,
1 'atol =',e12.3//' Initial y vector = ',9f5.1)
c
c Loop over all relevant values of mf.
do 193 moss = 0,2
do 192 meth = 1,2
do 191 miter = 0,3
if ( (miter.eq.0 .or. miter.eq.3) .and. moss.ne.0) go to 191
mf = 100*moss + 10*meth + miter
write (lout,100)
100 format(//80('*'))
c First run: nominal work array lengths, 3 output points.
irun = 1
lrw = 1000
liw = 90
nout = 3
110 continue
write (lout,120)mf,lrw,liw
120 format(//'Run with mf =',i4,'.',5x,
1 'Input work lengths lrw, liw =',2i6/)
do 125 i = 1,neq
125 y(i) = i
t = 0.0e0
tout = 1.0e0
istate = 1
ero = 0.0e0
c Loop over output points. Do output and accuracy check at each.
do 170 iout = 1,nout
call slsodes (fdem, neq, y, t, tout, itol, rtol, atol, itask,
1 istate, iopt, rwork, lrw, iwork, liw, jdem, mf)
nst = iwork(11)
hu = rwork(11)
nqu = iwork(14)
call edit (y, iout, erm)
write(lout,140)t,nst,hu,nqu,erm,(y(i),i=1,neq)
140 format('At t =',f5.1,3x,'nst =',i4,3x,'hu =',e12.3,3x,
1 'nqu =',i3,3x,' max. err. =',e11.3/
2 ' y array = ',4e15.6/5e15.6)
if (istate .lt. 0) go to 175
erm = erm/atol
ero = max(ero,erm)
if (erm .gt. 100.0e0) then
write (lout,150)
150 format(//' Warning: error exceeds 100 * tolerance'//)
nerr = nerr + 1
endif
tout = tout + 1.0e0
170 continue
175 continue
if (istate .lt. 0) nerr = nerr + 1
if (irun .eq. 2) go to 191
c Print final statistics (first run only)
nst = iwork(11)
nfe = iwork(12)
nje = iwork(13)
lenrw = iwork(17)
leniw = iwork(18)
nnz = iwork(19)
ngp = iwork(20)
nlu = iwork(21)
nzl = iwork(25)
nzu = iwork(26)
nfea = nfe
if (miter .eq. 2) nfea = nfe - ngp*nje
if (miter .eq. 3) nfea = nfe - nje
write (lout,180) lenrw,leniw,nst,nfe,nfea,nje,ero
180 format(/'Final statistics for this run:'/
1 ' rwork size =',i4,' iwork size =',i4/
2 ' number of steps =',i5/
3 ' number of f-s =',i5/
4 ' (excluding J-s) =',i5/
5 ' number of J-s =',i5/
6 ' error overrun =',e10.2)
if (miter .eq. 1 .or. miter .eq. 2)
1 write (lout,185)nnz,ngp,nlu,nzl,nzu
185 format(' number of nonzeros in J = ',i5/
1 ' number of J index groups =',i5/
2 ' number of LU decomp-s =',i5/
3 ' nonzeros in strict lower factor =',i5/
4 ' nonzeros in strict upper factor =',i5)
if (istate .lt. 0) go to 191
if (miter .eq. 1 .or. miter .eq. 2)
1 call ssout (neq, rwork(21), iwork, lout)
c Return for second run: minimal work array lengths, 1 output point.
irun = irun + 1
lrw = lenrw
liw = leniw
nout = 1
go to 110
191 continue
192 continue
193 continue
c
write (lout,100)
write (lout,200) nerr
200 format(//'Number of errors encountered =',i3)
stop
end
subroutine fdem (neq, t, y, ydot)
integer neq, i, igrid, j, l, m
real t, y, ydot
dimension y(neq), ydot(neq)
data igrid/3/
do 5 i = 1,neq
5 ydot(i) = 0.0e0
do 20 m = 1,igrid
do 10 l = 1,igrid
j = l + (m - 1)*igrid
if (m .ne. 1) ydot(j-igrid) = ydot(j-igrid) + y(j)
if (l .ne. 1) ydot(j-1) = ydot(j-1) + y(j)
ydot(j) = ydot(j) - 4.0e0*y(j)
if (l .ne. igrid) ydot(j+1) = ydot(j+1) + y(j)
10 continue
20 continue
return
end
subroutine jdem (neq, t, y, j, ia, ja, pdj)
integer neq, j, ia, ja, igrid, l, m
real t, y, pdj
dimension y(neq), ia(*), ja(*), pdj(neq)
data igrid/3/
m = (j - 1)/igrid + 1
l = j - (m - 1)*igrid
pdj(j) = -4.0e0
if (m .ne. 1) pdj(j-igrid) = 1.0e0
if (l .ne. 1) pdj(j-1) = 1.0e0
if (l .ne. igrid) pdj(j+1) = 1.0e0
return
end
subroutine edit (y, iout, erm)
integer iout, i, neq
real y, erm, er, yex
dimension y(*),yex(9,3)
data neq /9/
data yex /6.687279e-01, 9.901910e-01, 7.603061e-01,
1 8.077979e-01, 1.170226e+00, 8.810605e-01, 5.013331e-01,
2 7.201389e-01, 5.379644e-01, 1.340488e-01, 1.917157e-01,
3 1.374034e-01, 1.007882e-01, 1.437868e-01, 1.028010e-01,
4 3.844343e-02, 5.477593e-02, 3.911435e-02, 1.929166e-02,
5 2.735444e-02, 1.939611e-02, 1.055981e-02, 1.496753e-02,
6 1.060897e-02, 2.913689e-03, 4.128975e-03, 2.925977e-03/
erm = 0.0e0
do 10 i = 1,neq
er = abs(y(i) - yex(i,iout))
10 erm = max(erm,er)
return
end
subroutine ssout (neq, iwk, iwork, lout)
integer neq, iwk, iwork, lout
integer i, i1, i2, ipian, ipjan, nnz
dimension iwk(*), iwork(*)
ipian = iwork(23)
ipjan = iwork(24)
nnz = iwork(19)
i1 = ipian
i2 = i1 + neq
write (lout,10)(iwk(i),i=i1,i2)
10 format(/' structure descriptor array ian ='/(20i4))
i1 = ipjan
i2 = i1 + nnz - 1
write (lout,20)(iwk(i),i=i1,i2)
20 format(/' structure descriptor array jan ='/(20i4))
return
end
................................................................................
Demonstration problem for the DLSODES package
neq = 9 t0 = 0.0 rtol = 0.000E+00 atol = 0.100E-04
Initial y vector = 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0
********************************************************************************
Run with mf = 10. Input work lengths lrw, liw = 1000 90
At t = 1.0 nst = 42 hu = 0.241E-01 nqu = 4 max. err. = 0.394E-05
y array = 0.668730E+00 0.990188E+00 0.760308E+00 0.807799E+00
0.117023E+01 0.881061E+00 0.501332E+00 0.720142E+00 0.537962E+00
At t = 2.0 nst = 71 hu = 0.680E-01 nqu = 3 max. err. = 0.273E-04
y array = 0.134047E+00 0.191717E+00 0.137407E+00 0.100802E+00
0.143808E+00 0.102820E+00 0.384623E-01 0.548033E-01 0.391361E-01
At t = 3.0 nst = 90 hu = 0.455E-01 nqu = 3 max. err. = 0.121E-04
y array = 0.193008E-01 0.273568E-01 0.194059E-01 0.105663E-01
0.149796E-01 0.106158E-01 0.291803E-02 0.413489E-02 0.293048E-02
Final statistics for this run:
rwork size = 164 iwork size = 30
number of steps = 90
number of f-s = 98
(excluding J-s) = 98
number of J-s = 0
error overrun = 0.27E+01
Run with mf = 10. Input work lengths lrw, liw = 164 30
At t = 1.0 nst = 42 hu = 0.241E-01 nqu = 4 max. err. = 0.394E-05
y array = 0.668730E+00 0.990188E+00 0.760308E+00 0.807799E+00
0.117023E+01 0.881061E+00 0.501332E+00 0.720142E+00 0.537962E+00
********************************************************************************
Run with mf = 11. Input work lengths lrw, liw = 1000 90
At t = 1.0 nst = 27 hu = 0.862E-01 nqu = 5 max. err. = 0.988E-05
y array = 0.668727E+00 0.990190E+00 0.760307E+00 0.807796E+00
0.117022E+01 0.881060E+00 0.501339E+00 0.720139E+00 0.537974E+00
At t = 2.0 nst = 37 hu = 0.115E+00 nqu = 5 max. err. = 0.593E-05
y array = 0.134047E+00 0.191713E+00 0.137403E+00 0.100789E+00
0.143787E+00 0.102803E+00 0.384477E-01 0.547819E-01 0.391199E-01
At t = 3.0 nst = 44 hu = 0.155E+00 nqu = 5 max. err. = 0.386E-05
y array = 0.192920E-01 0.273552E-01 0.193970E-01 0.105624E-01
0.149714E-01 0.106120E-01 0.291609E-02 0.413247E-02 0.292857E-02
Final statistics for this run:
rwork size = 308 iwork size = 67
number of steps = 44
number of f-s = 56
(excluding J-s) = 56
number of J-s = 1
error overrun = 0.99E+00
number of nonzeros in J = 27
number of J index groups = 0
number of LU decomp-s = 9
nonzeros in strict lower factor = 8
nonzeros in strict upper factor = 14
structure descriptor array ian =
1 3 6 8 11 15 18 21 25 28
structure descriptor array jan =
1 2 3 1 2 3 2 1 5 4 2 6 5 4 3 6 5 7 4 8
9 7 5 8 9 6 8
Run with mf = 11. Input work lengths lrw, liw = 308 67
At t = 1.0 nst = 27 hu = 0.862E-01 nqu = 5 max. err. = 0.988E-05
y array = 0.668727E+00 0.990190E+00 0.760307E+00 0.807796E+00
0.117022E+01 0.881060E+00 0.501339E+00 0.720139E+00 0.537974E+00
********************************************************************************
Run with mf = 12. Input work lengths lrw, liw = 1000 90
At t = 1.0 nst = 27 hu = 0.862E-01 nqu = 5 max. err. = 0.988E-05
y array = 0.668727E+00 0.990190E+00 0.760307E+00 0.807796E+00
0.117022E+01 0.881060E+00 0.501339E+00 0.720139E+00 0.537974E+00
At t = 2.0 nst = 37 hu = 0.115E+00 nqu = 5 max. err. = 0.593E-05
y array = 0.134047E+00 0.191713E+00 0.137403E+00 0.100789E+00
0.143787E+00 0.102803E+00 0.384477E-01 0.547819E-01 0.391199E-01
At t = 3.0 nst = 44 hu = 0.155E+00 nqu = 5 max. err. = 0.386E-05
y array = 0.192920E-01 0.273552E-01 0.193970E-01 0.105624E-01
0.149714E-01 0.106120E-01 0.291609E-02 0.413247E-02 0.292857E-02
Final statistics for this run:
rwork size = 315 iwork size = 67
number of steps = 44
number of f-s = 60
(excluding J-s) = 56
number of J-s = 1
error overrun = 0.99E+00
number of nonzeros in J = 27
number of J index groups = 4
number of LU decomp-s = 9
nonzeros in strict lower factor = 8
nonzeros in strict upper factor = 14
structure descriptor array ian =
1 3 6 8 11 15 18 21 25 28
structure descriptor array jan =
1 2 3 1 2 3 2 1 5 4 2 6 5 4 3 6 5 7 4 8
9 7 5 8 9 6 8
Run with mf = 12. Input work lengths lrw, liw = 315 67
At t = 1.0 nst = 27 hu = 0.862E-01 nqu = 5 max. err. = 0.988E-05
y array = 0.668727E+00 0.990190E+00 0.760307E+00 0.807796E+00
0.117022E+01 0.881060E+00 0.501339E+00 0.720139E+00 0.537974E+00
********************************************************************************
Run with mf = 13. Input work lengths lrw, liw = 1000 90
At t = 1.0 nst = 28 hu = 0.825E-01 nqu = 5 max. err. = 0.591E-05
y array = 0.668729E+00 0.990192E+00 0.760304E+00 0.807797E+00
0.117022E+01 0.881060E+00 0.501334E+00 0.720136E+00 0.537970E+00
At t = 2.0 nst = 41 hu = 0.825E-01 nqu = 5 max. err. = 0.468E-05
y array = 0.134048E+00 0.191713E+00 0.137405E+00 0.100784E+00
0.143782E+00 0.102798E+00 0.384467E-01 0.547752E-01 0.391129E-01
At t = 3.0 nst = 58 hu = 0.536E-01 nqu = 4 max. err. = 0.801E-04
y array = 0.193021E-01 0.273573E-01 0.194762E-01 0.105617E-01
0.149669E-01 0.106567E-01 0.291302E-02 0.412818E-02 0.292528E-02
Final statistics for this run:
rwork size = 175 iwork size = 30
number of steps = 58
number of f-s = 90
(excluding J-s) = 80
number of J-s = 10
error overrun = 0.80E+01
Run with mf = 13. Input work lengths lrw, liw = 175 30
At t = 1.0 nst = 28 hu = 0.825E-01 nqu = 5 max. err. = 0.591E-05
y array = 0.668729E+00 0.990192E+00 0.760304E+00 0.807797E+00
0.117022E+01 0.881060E+00 0.501334E+00 0.720136E+00 0.537970E+00
********************************************************************************
Run with mf = 20. Input work lengths lrw, liw = 1000 90
At t = 1.0 nst = 39 hu = 0.549E-01 nqu = 5 max. err. = 0.378E-04
y array = 0.668726E+00 0.990193E+00 0.760309E+00 0.807791E+00
0.117020E+01 0.881056E+00 0.501356E+00 0.720124E+00 0.538002E+00
At t = 2.0 nst = 53 hu = 0.677E-01 nqu = 5 max. err. = 0.113E-04
y array = 0.134039E+00 0.191719E+00 0.137397E+00 0.100792E+00
0.143779E+00 0.102808E+00 0.384485E-01 0.547872E-01 0.391222E-01
At t = 3.0 nst = 64 hu = 0.123E+00 nqu = 5 max. err. = 0.869E-05
y array = 0.192944E-01 0.273518E-01 0.193999E-01 0.105634E-01
0.149762E-01 0.106132E-01 0.291807E-02 0.413507E-02 0.293054E-02
Final statistics for this run:
rwork size = 101 iwork size = 30
number of steps = 64
number of f-s = 77
(excluding J-s) = 77
number of J-s = 0
error overrun = 0.38E+01
Run with mf = 20. Input work lengths lrw, liw = 101 30
At t = 1.0 nst = 39 hu = 0.549E-01 nqu = 5 max. err. = 0.378E-04
y array = 0.668726E+00 0.990193E+00 0.760309E+00 0.807791E+00
0.117020E+01 0.881056E+00 0.501356E+00 0.720124E+00 0.538002E+00
********************************************************************************
Run with mf = 21. Input work lengths lrw, liw = 1000 90
At t = 1.0 nst = 38 hu = 0.573E-01 nqu = 5 max. err. = 0.254E-04
y array = 0.668726E+00 0.990191E+00 0.760308E+00 0.807793E+00
0.117021E+01 0.881059E+00 0.501348E+00 0.720133E+00 0.537990E+00
At t = 2.0 nst = 52 hu = 0.105E+00 nqu = 5 max. err. = 0.132E-04
y array = 0.134044E+00 0.191709E+00 0.137402E+00 0.100788E+00
0.143786E+00 0.102805E+00 0.384531E-01 0.547890E-01 0.391276E-01
At t = 3.0 nst = 61 hu = 0.132E+00 nqu = 5 max. err. = 0.134E-04
y array = 0.192907E-01 0.273543E-01 0.193977E-01 0.105672E-01
0.149788E-01 0.106186E-01 0.292280E-02 0.414233E-02 0.293619E-02
Final statistics for this run:
rwork size = 245 iwork size = 67
number of steps = 61
number of f-s = 71
(excluding J-s) = 71
number of J-s = 2
error overrun = 0.25E+01
number of nonzeros in J = 27
number of J index groups = 0
number of LU decomp-s = 8
nonzeros in strict lower factor = 8
nonzeros in strict upper factor = 14
structure descriptor array ian =
1 3 6 8 11 15 18 21 25 28
structure descriptor array jan =
1 2 3 1 2 3 2 1 5 4 2 6 5 4 3 6 5 7 4 8
9 7 5 8 9 6 8
Run with mf = 21. Input work lengths lrw, liw = 245 67
At t = 1.0 nst = 38 hu = 0.573E-01 nqu = 5 max. err. = 0.254E-04
y array = 0.668726E+00 0.990191E+00 0.760308E+00 0.807793E+00
0.117021E+01 0.881059E+00 0.501348E+00 0.720133E+00 0.537990E+00
********************************************************************************
Run with mf = 22. Input work lengths lrw, liw = 1000 90
At t = 1.0 nst = 38 hu = 0.573E-01 nqu = 5 max. err. = 0.254E-04
y array = 0.668726E+00 0.990191E+00 0.760308E+00 0.807793E+00
0.117021E+01 0.881059E+00 0.501348E+00 0.720133E+00 0.537990E+00
At t = 2.0 nst = 52 hu = 0.105E+00 nqu = 5 max. err. = 0.132E-04
y array = 0.134044E+00 0.191709E+00 0.137402E+00 0.100788E+00
0.143786E+00 0.102805E+00 0.384531E-01 0.547890E-01 0.391276E-01
At t = 3.0 nst = 61 hu = 0.132E+00 nqu = 5 max. err. = 0.134E-04
y array = 0.192907E-01 0.273543E-01 0.193977E-01 0.105672E-01
0.149788E-01 0.106186E-01 0.292280E-02 0.414233E-02 0.293619E-02
Final statistics for this run:
rwork size = 252 iwork size = 67
number of steps = 61
number of f-s = 79
(excluding J-s) = 71
number of J-s = 2
error overrun = 0.25E+01
number of nonzeros in J = 27
number of J index groups = 4
number of LU decomp-s = 8
nonzeros in strict lower factor = 8
nonzeros in strict upper factor = 14
structure descriptor array ian =
1 3 6 8 11 15 18 21 25 28
structure descriptor array jan =
1 2 3 1 2 3 2 1 5 4 2 6 5 4 3 6 5 7 4 8
9 7 5 8 9 6 8
Run with mf = 22. Input work lengths lrw, liw = 252 67
At t = 1.0 nst = 38 hu = 0.573E-01 nqu = 5 max. err. = 0.254E-04
y array = 0.668726E+00 0.990191E+00 0.760308E+00 0.807793E+00
0.117021E+01 0.881059E+00 0.501348E+00 0.720133E+00 0.537990E+00
********************************************************************************
Run with mf = 23. Input work lengths lrw, liw = 1000 90
At t = 1.0 nst = 39 hu = 0.564E-01 nqu = 5 max. err. = 0.334E-04
y array = 0.668727E+00 0.990191E+00 0.760307E+00 0.807793E+00
0.117019E+01 0.881055E+00 0.501339E+00 0.720129E+00 0.537977E+00
At t = 2.0 nst = 53 hu = 0.720E-01 nqu = 5 max. err. = 0.268E-04
y array = 0.134056E+00 0.191713E+00 0.137402E+00 0.100785E+00
0.143781E+00 0.102798E+00 0.384437E-01 0.548027E-01 0.391161E-01
At t = 3.0 nst = 80 hu = 0.200E-01 nqu = 4 max. err. = 0.490E-04
y array = 0.192918E-01 0.273431E-01 0.194010E-01 0.105628E-01
0.149652E-01 0.106029E-01 0.290678E-02 0.412271E-02 0.297494E-02
Final statistics for this run:
rwork size = 112 iwork size = 30
number of steps = 80
number of f-s = 137
(excluding J-s) = 122
number of J-s = 15
error overrun = 0.49E+01
Run with mf = 23. Input work lengths lrw, liw = 112 30
At t = 1.0 nst = 39 hu = 0.564E-01 nqu = 5 max. err. = 0.334E-04
y array = 0.668727E+00 0.990191E+00 0.760307E+00 0.807793E+00
0.117019E+01 0.881055E+00 0.501339E+00 0.720129E+00 0.537977E+00
********************************************************************************
Run with mf = 111. Input work lengths lrw, liw = 1000 90
At t = 1.0 nst = 27 hu = 0.862E-01 nqu = 5 max. err. = 0.988E-05
y array = 0.668727E+00 0.990190E+00 0.760307E+00 0.807796E+00
0.117022E+01 0.881060E+00 0.501339E+00 0.720139E+00 0.537974E+00
At t = 2.0 nst = 37 hu = 0.115E+00 nqu = 5 max. err. = 0.593E-05
y array = 0.134047E+00 0.191713E+00 0.137403E+00 0.100789E+00
0.143787E+00 0.102803E+00 0.384477E-01 0.547819E-01 0.391199E-01
At t = 3.0 nst = 44 hu = 0.155E+00 nqu = 5 max. err. = 0.386E-05
y array = 0.192920E-01 0.273552E-01 0.193970E-01 0.105624E-01
0.149714E-01 0.106120E-01 0.291609E-02 0.413247E-02 0.292857E-02
Final statistics for this run:
rwork size = 308 iwork size = 30
number of steps = 44
number of f-s = 56
(excluding J-s) = 56
number of J-s = 1
error overrun = 0.99E+00
number of nonzeros in J = 27
number of J index groups = 0
number of LU decomp-s = 9
nonzeros in strict lower factor = 8
nonzeros in strict upper factor = 14
structure descriptor array ian =
1 3 6 8 11 15 18 21 25 28
structure descriptor array jan =
1 2 3 1 2 3 2 1 5 4 2 6 5 4 3 6 5 7 4 8
9 7 5 8 9 6 8
Run with mf = 111. Input work lengths lrw, liw = 308 30
At t = 1.0 nst = 27 hu = 0.862E-01 nqu = 5 max. err. = 0.988E-05
y array = 0.668727E+00 0.990190E+00 0.760307E+00 0.807796E+00
0.117022E+01 0.881060E+00 0.501339E+00 0.720139E+00 0.537974E+00
********************************************************************************
Run with mf = 112. Input work lengths lrw, liw = 1000 90
At t = 1.0 nst = 27 hu = 0.862E-01 nqu = 5 max. err. = 0.988E-05
y array = 0.668727E+00 0.990190E+00 0.760307E+00 0.807796E+00
0.117022E+01 0.881060E+00 0.501339E+00 0.720139E+00 0.537974E+00
At t = 2.0 nst = 37 hu = 0.115E+00 nqu = 5 max. err. = 0.593E-05
y array = 0.134047E+00 0.191713E+00 0.137403E+00 0.100789E+00
0.143787E+00 0.102803E+00 0.384477E-01 0.547819E-01 0.391199E-01
At t = 3.0 nst = 44 hu = 0.155E+00 nqu = 5 max. err. = 0.386E-05
y array = 0.192920E-01 0.273552E-01 0.193970E-01 0.105624E-01
0.149714E-01 0.106120E-01 0.291609E-02 0.413247E-02 0.292857E-02
Final statistics for this run:
rwork size = 315 iwork size = 30
number of steps = 44
number of f-s = 60
(excluding J-s) = 56
number of J-s = 1
error overrun = 0.99E+00
number of nonzeros in J = 27
number of J index groups = 4
number of LU decomp-s = 9
nonzeros in strict lower factor = 8
nonzeros in strict upper factor = 14
structure descriptor array ian =
1 3 6 8 11 15 18 21 25 28
structure descriptor array jan =
1 2 3 1 2 3 2 1 5 4 2 6 5 4 3 6 5 7 4 8
9 7 5 8 9 6 8
Run with mf = 112. Input work lengths lrw, liw = 315 30
At t = 1.0 nst = 27 hu = 0.862E-01 nqu = 5 max. err. = 0.988E-05
y array = 0.668727E+00 0.990190E+00 0.760307E+00 0.807796E+00
0.117022E+01 0.881060E+00 0.501339E+00 0.720139E+00 0.537974E+00
********************************************************************************
Run with mf = 121. Input work lengths lrw, liw = 1000 90
At t = 1.0 nst = 38 hu = 0.573E-01 nqu = 5 max. err. = 0.254E-04
y array = 0.668726E+00 0.990191E+00 0.760308E+00 0.807793E+00
0.117021E+01 0.881059E+00 0.501348E+00 0.720133E+00 0.537990E+00
At t = 2.0 nst = 52 hu = 0.105E+00 nqu = 5 max. err. = 0.132E-04
y array = 0.134044E+00 0.191709E+00 0.137402E+00 0.100788E+00
0.143786E+00 0.102805E+00 0.384531E-01 0.547890E-01 0.391276E-01
At t = 3.0 nst = 61 hu = 0.132E+00 nqu = 5 max. err. = 0.134E-04
y array = 0.192907E-01 0.273543E-01 0.193977E-01 0.105672E-01
0.149788E-01 0.106186E-01 0.292280E-02 0.414233E-02 0.293619E-02
Final statistics for this run:
rwork size = 245 iwork size = 30
number of steps = 61
number of f-s = 71
(excluding J-s) = 71
number of J-s = 2
error overrun = 0.25E+01
number of nonzeros in J = 27
number of J index groups = 0
number of LU decomp-s = 8
nonzeros in strict lower factor = 8
nonzeros in strict upper factor = 14
structure descriptor array ian =
1 3 6 8 11 15 18 21 25 28
structure descriptor array jan =
1 2 3 1 2 3 2 1 5 4 2 6 5 4 3 6 5 7 4 8
9 7 5 8 9 6 8
Run with mf = 121. Input work lengths lrw, liw = 245 30
At t = 1.0 nst = 38 hu = 0.573E-01 nqu = 5 max. err. = 0.254E-04
y array = 0.668726E+00 0.990191E+00 0.760308E+00 0.807793E+00
0.117021E+01 0.881059E+00 0.501348E+00 0.720133E+00 0.537990E+00
********************************************************************************
Run with mf = 122. Input work lengths lrw, liw = 1000 90
At t = 1.0 nst = 38 hu = 0.573E-01 nqu = 5 max. err. = 0.254E-04
y array = 0.668726E+00 0.990191E+00 0.760308E+00 0.807793E+00
0.117021E+01 0.881059E+00 0.501348E+00 0.720133E+00 0.537990E+00
At t = 2.0 nst = 52 hu = 0.105E+00 nqu = 5 max. err. = 0.132E-04
y array = 0.134044E+00 0.191709E+00 0.137402E+00 0.100788E+00
0.143786E+00 0.102805E+00 0.384531E-01 0.547890E-01 0.391276E-01
At t = 3.0 nst = 61 hu = 0.132E+00 nqu = 5 max. err. = 0.134E-04
y array = 0.192907E-01 0.273543E-01 0.193977E-01 0.105672E-01
0.149788E-01 0.106186E-01 0.292280E-02 0.414233E-02 0.293619E-02
Final statistics for this run:
rwork size = 252 iwork size = 30
number of steps = 61
number of f-s = 79
(excluding J-s) = 71
number of J-s = 2
error overrun = 0.25E+01
number of nonzeros in J = 27
number of J index groups = 4
number of LU decomp-s = 8
nonzeros in strict lower factor = 8
nonzeros in strict upper factor = 14
structure descriptor array ian =
1 3 6 8 11 15 18 21 25 28
structure descriptor array jan =
1 2 3 1 2 3 2 1 5 4 2 6 5 4 3 6 5 7 4 8
9 7 5 8 9 6 8
Run with mf = 122. Input work lengths lrw, liw = 252 30
At t = 1.0 nst = 38 hu = 0.573E-01 nqu = 5 max. err. = 0.254E-04
y array = 0.668726E+00 0.990191E+00 0.760308E+00 0.807793E+00
0.117021E+01 0.881059E+00 0.501348E+00 0.720133E+00 0.537990E+00
********************************************************************************
Run with mf = 211. Input work lengths lrw, liw = 1000 90
At t = 1.0 nst = 27 hu = 0.862E-01 nqu = 5 max. err. = 0.988E-05
y array = 0.668727E+00 0.990190E+00 0.760307E+00 0.807796E+00
0.117022E+01 0.881060E+00 0.501339E+00 0.720139E+00 0.537974E+00
At t = 2.0 nst = 37 hu = 0.115E+00 nqu = 5 max. err. = 0.593E-05
y array = 0.134047E+00 0.191713E+00 0.137403E+00 0.100789E+00
0.143787E+00 0.102803E+00 0.384477E-01 0.547819E-01 0.391199E-01
At t = 3.0 nst = 44 hu = 0.155E+00 nqu = 5 max. err. = 0.386E-05
y array = 0.192920E-01 0.273552E-01 0.193970E-01 0.105624E-01
0.149714E-01 0.106120E-01 0.291609E-02 0.413247E-02 0.292857E-02
Final statistics for this run:
rwork size = 308 iwork size = 30
number of steps = 44
number of f-s = 56
(excluding J-s) = 56
number of J-s = 1
error overrun = 0.99E+00
number of nonzeros in J = 27
number of J index groups = 0
number of LU decomp-s = 9
nonzeros in strict lower factor = 8
nonzeros in strict upper factor = 14
structure descriptor array ian =
1 3 6 8 11 15 18 21 25 28
structure descriptor array jan =
1 2 3 1 2 3 2 1 5 4 2 6 5 4 3 6 5 7 4 8
9 7 5 8 9 6 8
Run with mf = 211. Input work lengths lrw, liw = 308 30
At t = 1.0 nst = 27 hu = 0.862E-01 nqu = 5 max. err. = 0.988E-05
y array = 0.668727E+00 0.990190E+00 0.760307E+00 0.807796E+00
0.117022E+01 0.881060E+00 0.501339E+00 0.720139E+00 0.537974E+00
********************************************************************************
Run with mf = 212. Input work lengths lrw, liw = 1000 90
At t = 1.0 nst = 27 hu = 0.862E-01 nqu = 5 max. err. = 0.988E-05
y array = 0.668727E+00 0.990190E+00 0.760307E+00 0.807796E+00
0.117022E+01 0.881060E+00 0.501339E+00 0.720139E+00 0.537974E+00
At t = 2.0 nst = 37 hu = 0.115E+00 nqu = 5 max. err. = 0.593E-05
y array = 0.134047E+00 0.191713E+00 0.137403E+00 0.100789E+00
0.143787E+00 0.102803E+00 0.384477E-01 0.547819E-01 0.391199E-01
At t = 3.0 nst = 44 hu = 0.155E+00 nqu = 5 max. err. = 0.386E-05
y array = 0.192920E-01 0.273552E-01 0.193970E-01 0.105624E-01
0.149714E-01 0.106120E-01 0.291609E-02 0.413247E-02 0.292857E-02
Final statistics for this run:
rwork size = 315 iwork size = 30
number of steps = 44
number of f-s = 60
(excluding J-s) = 56
number of J-s = 1
error overrun = 0.99E+00
number of nonzeros in J = 27
number of J index groups = 4
number of LU decomp-s = 9
nonzeros in strict lower factor = 8
nonzeros in strict upper factor = 14
structure descriptor array ian =
1 3 6 8 11 15 18 21 25 28
structure descriptor array jan =
1 2 3 1 2 3 2 1 5 4 2 6 5 4 3 6 5 7 4 8
9 7 5 8 9 6 8
Run with mf = 212. Input work lengths lrw, liw = 315 30
At t = 1.0 nst = 27 hu = 0.862E-01 nqu = 5 max. err. = 0.988E-05
y array = 0.668727E+00 0.990190E+00 0.760307E+00 0.807796E+00
0.117022E+01 0.881060E+00 0.501339E+00 0.720139E+00 0.537974E+00
********************************************************************************
Run with mf = 221. Input work lengths lrw, liw = 1000 90
At t = 1.0 nst = 38 hu = 0.573E-01 nqu = 5 max. err. = 0.254E-04
y array = 0.668726E+00 0.990191E+00 0.760308E+00 0.807793E+00
0.117021E+01 0.881059E+00 0.501348E+00 0.720133E+00 0.537990E+00
At t = 2.0 nst = 52 hu = 0.105E+00 nqu = 5 max. err. = 0.132E-04
y array = 0.134044E+00 0.191709E+00 0.137402E+00 0.100788E+00
0.143786E+00 0.102805E+00 0.384531E-01 0.547890E-01 0.391276E-01
At t = 3.0 nst = 61 hu = 0.132E+00 nqu = 5 max. err. = 0.134E-04
y array = 0.192907E-01 0.273543E-01 0.193977E-01 0.105672E-01
0.149788E-01 0.106186E-01 0.292280E-02 0.414233E-02 0.293619E-02
Final statistics for this run:
rwork size = 245 iwork size = 30
number of steps = 61
number of f-s = 71
(excluding J-s) = 71
number of J-s = 2
error overrun = 0.25E+01
number of nonzeros in J = 27
number of J index groups = 0
number of LU decomp-s = 8
nonzeros in strict lower factor = 8
nonzeros in strict upper factor = 14
structure descriptor array ian =
1 3 6 8 11 15 18 21 25 28
structure descriptor array jan =
1 2 3 1 2 3 2 1 5 4 2 6 5 4 3 6 5 7 4 8
9 7 5 8 9 6 8
Run with mf = 221. Input work lengths lrw, liw = 245 30
At t = 1.0 nst = 38 hu = 0.573E-01 nqu = 5 max. err. = 0.254E-04
y array = 0.668726E+00 0.990191E+00 0.760308E+00 0.807793E+00
0.117021E+01 0.881059E+00 0.501348E+00 0.720133E+00 0.537990E+00
********************************************************************************
Run with mf = 222. Input work lengths lrw, liw = 1000 90
At t = 1.0 nst = 38 hu = 0.573E-01 nqu = 5 max. err. = 0.254E-04
y array = 0.668726E+00 0.990191E+00 0.760308E+00 0.807793E+00
0.117021E+01 0.881059E+00 0.501348E+00 0.720133E+00 0.537990E+00
At t = 2.0 nst = 52 hu = 0.105E+00 nqu = 5 max. err. = 0.132E-04
y array = 0.134044E+00 0.191709E+00 0.137402E+00 0.100788E+00
0.143786E+00 0.102805E+00 0.384531E-01 0.547890E-01 0.391276E-01
At t = 3.0 nst = 61 hu = 0.132E+00 nqu = 5 max. err. = 0.134E-04
y array = 0.192907E-01 0.273543E-01 0.193977E-01 0.105672E-01
0.149788E-01 0.106186E-01 0.292280E-02 0.414233E-02 0.293619E-02
Final statistics for this run:
rwork size = 252 iwork size = 30
number of steps = 61
number of f-s = 79
(excluding J-s) = 71
number of J-s = 2
error overrun = 0.25E+01
number of nonzeros in J = 27
number of J index groups = 4
number of LU decomp-s = 8
nonzeros in strict lower factor = 8
nonzeros in strict upper factor = 14
structure descriptor array ian =
1 3 6 8 11 15 18 21 25 28
structure descriptor array jan =
1 2 3 1 2 3 2 1 5 4 2 6 5 4 3 6 5 7 4 8
9 7 5 8 9 6 8
Run with mf = 222. Input work lengths lrw, liw = 252 30
At t = 1.0 nst = 38 hu = 0.573E-01 nqu = 5 max. err. = 0.254E-04
y array = 0.668726E+00 0.990191E+00 0.760308E+00 0.807793E+00
0.117021E+01 0.881059E+00 0.501348E+00 0.720133E+00 0.537990E+00
********************************************************************************
Number of errors encountered = 0
==========Source and Output for LSODA Demonstration Program=====================
c-----------------------------------------------------------------------
c Demonstration program for the SLSODA package.
c This is the version of 13 June 2001.
c
c This version is in single precision.
c
c The package is used to solve two simple problems,
c one with a full Jacobian, the other with a banded Jacobian,
c with the 2 appropriate values of jt in each case.
c If the errors are too large, or other difficulty occurs,
c a warning message is printed. All output is on unit lout = 6.
c-----------------------------------------------------------------------
external f1, jac1, f2, jac2
integer i, iopar, iopt, iout, istate, itask, itol, iwork,
1 jt, leniw, lenrw, liw, lout, lrw, mband, mused,
2 ml, mu, neq, nerr, nfe, nfea, nje, nout, nqu, nst
real atol, dtout, dtout0, dtout1, er, erm, ero, hu,
1 rtol, rwork, t, tout, tout1, tsw, y
dimension y(25), rwork(522), iwork(45)
data lout/6/, tout1/16.921743e0/, dtout/17.341162e0/
c
nerr = 0
itol = 1
rtol = 0.0e0
atol = 1.0e-8
lrw = 522
liw = 45
iopt = 0
c
c First problem
c
neq = 2
nout = 4
write (lout,110) neq,itol,rtol,atol
110 format(/'Demonstration program for SLSODA package'////
1 ' Problem 1: Van der Pol oscillator:'/
2 ' xdotdot - 20*(1 - x**2)*xdot + x = 0, ',
3 ' x(0) = 2, xdot(0) = 0'/' neq =',i2/
4 ' itol =',i3,' rtol =',e10.1,' atol =',e10.1//)
c
do 190 jt = 1,2
write (lout,120) jt
120 format(//' Solution with jt =',i3//
1 ' t x xdot meth',
2 ' nq h tsw'//)
t = 0.0e0
y(1) = 2.0e0
y(2) = 0.0e0
itask = 1
istate = 1
dtout0 = 0.5e0*tout1
dtout1 = 0.5e0*dtout
tout = dtout0
ero = 0.0e0
do 170 iout = 1,nout
call slsoda(f1,neq,y,t,tout,itol,rtol,atol,itask,istate,
1 iopt,rwork,lrw,iwork,liw,jac1,jt)
hu = rwork(11)
tsw = rwork(15)
nqu = iwork(14)
mused = iwork(19)
write (lout,140) t,y(1),y(2),mused,nqu,hu,tsw
140 format(e12.5,e16.5,e14.3,2i6,2e13.3)
if (istate .lt. 0) go to 175
iopar = iout - 2*(iout/2)
if (iopar .ne. 0) go to 160
er = abs(y(1))
ero = max(ero,er)
if (er .gt. 1.0e-2) then
write (lout,150)
150 format(//' Warning: value at root exceeds 1.0e-2'//)
nerr = nerr + 1
endif
160 if (iout .eq. 1) tout = tout + dtout0
if (iout .gt. 1) tout = tout + dtout1
170 continue
175 continue
if (istate .lt. 0) nerr = nerr + 1
nst = iwork(11)
nfe = iwork(12)
nje = iwork(13)
lenrw = iwork(17)
leniw = iwork(18)
nfea = nfe
if (jt .eq. 2) nfea = nfe - neq*nje
write (lout,180) lenrw,leniw,nst,nfe,nfea,nje,ero
180 format(//' Final statistics for this run:'/
1 ' rwork size =',i4,' iwork size =',i4/
2 ' number of steps =',i5/
3 ' number of f-s =',i5/
4 ' (excluding J-s) =',i5/
5 ' number of J-s =',i5/
6 ' max. error at root =',e10.2)
190 continue
c
c Second problem
c
neq = 25
ml = 5
mu = 0
iwork(1) = ml
iwork(2) = mu
mband = ml + mu + 1
atol = 1.0e-6
nout = 5
write (lout,210) neq,ml,mu,itol,rtol,atol
210 format(///80('-')///
1 ' Problem 2: ydot = A * y , where',
2 ' A is a banded lower triangular matrix'/
2 ' derived from 2-D advection PDE'/
3 ' neq =',i3,' ml =',i2,' mu =',i2/
4 ' itol =',i3,' rtol =',e10.1,' atol =',e10.1//)
do 290 jt = 4,5
write (lout,220) jt
220 format(//' Solution with jt =',i3//
1 ' t max.err. meth ',
2 'nq h tsw'//)
t = 0.0e0
do 230 i = 2,neq
230 y(i) = 0.0e0
y(1) = 1.0e0
itask = 1
istate = 1
tout = 0.01e0
ero = 0.0e0
do 270 iout = 1,nout
call slsoda(f2,neq,y,t,tout,itol,rtol,atol,itask,istate,
1 iopt,rwork,lrw,iwork,liw,jac2,jt)
call edit2(y,t,erm)
hu = rwork(11)
tsw = rwork(15)
nqu = iwork(14)
mused = iwork(19)
write (lout,240) t,erm,mused,nqu,hu,tsw
240 format(e15.5,e14.3,2i6,2e14.3)
if (istate .lt. 0) go to 275
er = erm/atol
ero = max(ero,er)
if (er .gt. 1000.0e0) then
write (lout,150)
nerr = nerr + 1
endif
270 tout = tout*10.0e0
275 continue
if (istate .lt. 0) nerr = nerr + 1
nst = iwork(11)
nfe = iwork(12)
nje = iwork(13)
lenrw = iwork(17)
leniw = iwork(18)
nfea = nfe
if (jt .eq. 5) nfea = nfe - mband*nje
write (lout,280) lenrw,leniw,nst,nfe,nfea,nje,ero
280 format(//' Final statistics for this run:'/
1 ' rwork size =',i4,' iwork size =',i4/
2 ' number of steps =',i5/
3 ' number of f-s =',i5/
4 ' (excluding J-s) =',i5/
5 ' number of J-s =',i5/
6 ' error overrun =',e10.2)
290 continue
write (lout,300) nerr
300 format(///' Number of errors encountered =',i3)
stop
end
subroutine f1 (neq, t, y, ydot)
integer neq
real t, y, ydot
dimension y(neq), ydot(neq)
ydot(1) = y(2)
ydot(2) = 20.0e0*(1.0e0 - y(1)*y(1))*y(2) - y(1)
return
end
subroutine jac1 (neq, t, y, ml, mu, pd, nrowpd)
integer neq, ml, mu, nrowpd
real t, y, pd
dimension y(neq), pd(nrowpd,neq)
pd(1,1) = 0.0e0
pd(1,2) = 1.0e0
pd(2,1) = -40.0e0*y(1)*y(2) - 1.0e0
pd(2,2) = 20.0e0*(1.0e0 - y(1)*y(1))
return
end
subroutine f2 (neq, t, y, ydot)
integer neq, i, j, k, ng
real t, y, ydot, alph1, alph2, d
dimension y(neq), ydot(neq)
data alph1/1.0e0/, alph2/1.0e0/, ng/5/
do 10 j = 1,ng
do 10 i = 1,ng
k = i + (j - 1)*ng
d = -2.0e0*y(k)
if (i .ne. 1) d = d + y(k-1)*alph1
if (j .ne. 1) d = d + y(k-ng)*alph2
10 ydot(k) = d
return
end
subroutine jac2 (neq, t, y, ml, mu, pd, nrowpd)
integer neq, ml, mu, nrowpd, j, mband, mu1, mu2, ng
real t, y, pd, alph1, alph2
dimension y(neq), pd(nrowpd,neq)
data alph1/1.0e0/, alph2/1.0e0/, ng/5/
mband = ml + mu + 1
mu1 = mu + 1
mu2 = mu + 2
do 10 j = 1,neq
pd(mu1,j) = -2.0e0
pd(mu2,j) = alph1
10 pd(mband,j) = alph2
do 20 j = ng,neq,ng
20 pd(mu2,j) = 0.0e0
return
end
subroutine edit2 (y, t, erm)
integer i, j, k, ng
real y, t, erm, alph1, alph2, a1, a2, er, ex, yt
dimension y(*)
data alph1/1.0e0/, alph2/1.0e0/, ng/5/
erm = 0.0e0
if (t .eq. 0.0e0) return
ex = 0.0e0
if (t .le. 30.0e0) ex = exp(-2.0e0*t)
a2 = 1.0e0
do 60 j = 1,ng
a1 = 1.0e0
do 50 i = 1,ng
k = i + (j - 1)*ng
yt = t**(i+j-2)*ex*a1*a2
er = abs(y(k)-yt)
erm = max(erm,er)
a1 = a1*alph1/i
50 continue
a2 = a2*alph2/j
60 continue
return
end
................................................................................
Demonstration program for DLSODA package
Problem 1: Van der Pol oscillator:
xdotdot - 20*(1 - x**2)*xdot + x = 0, x(0) = 2, xdot(0) = 0
neq = 2
itol = 1 rtol = 0.0E+00 atol = 0.1E-07
Solution with jt = 1
t x xdot meth nq h tsw
0.84609E+01 0.16731E+01 -0.464E-01 2 4 0.209E+00 0.311E+00
0.16922E+02 -0.11574E-03 -0.141E+02 1 7 0.206E-02 0.158E+02
0.25592E+02 -0.16828E+01 0.459E-01 2 4 0.240E+00 0.174E+02
0.34263E+02 0.21448E-03 0.141E+02 1 8 0.293E-02 0.332E+02
Final statistics for this run:
rwork size = 52 iwork size = 22
number of steps = 695
number of f-s = 1305
(excluding J-s) = 1305
number of J-s = 30
max. error at root = 0.21E-03
Solution with jt = 2
t x xdot meth nq h tsw
0.84609E+01 0.16731E+01 -0.464E-01 2 4 0.209E+00 0.311E+00
0.16922E+02 -0.11574E-03 -0.141E+02 1 7 0.206E-02 0.158E+02
0.25592E+02 -0.16828E+01 0.459E-01 2 4 0.240E+00 0.174E+02
0.34263E+02 0.21448E-03 0.141E+02 1 8 0.293E-02 0.332E+02
Final statistics for this run:
rwork size = 52 iwork size = 22
number of steps = 695
number of f-s = 1365
(excluding J-s) = 1305
number of J-s = 30
max. error at root = 0.21E-03
--------------------------------------------------------------------------------
Problem 2: ydot = A * y , where A is a banded lower triangular matrix
derived from 2-D advection PDE
neq = 25 ml = 5 mu = 0
itol = 1 rtol = 0.0E+00 atol = 0.1E-05
Solution with jt = 4
t max.err. meth nq h tsw
0.10000E-01 0.476E-06 1 2 0.714E-02 0.000E+00
0.10000E+00 0.988E-06 1 4 0.343E-01 0.000E+00
0.10000E+01 0.431E-06 1 5 0.724E-01 0.000E+00
0.10000E+02 0.558E-07 1 3 0.323E+00 0.000E+00
0.10000E+03 0.127E-11 2 1 0.239E+03 0.170E+02
Final statistics for this run:
rwork size = 522 iwork size = 45
number of steps = 105
number of f-s = 207
(excluding J-s) = 207
number of J-s = 3
error overrun = 0.99E+00
Solution with jt = 5
t max.err. meth nq h tsw
0.10000E-01 0.476E-06 1 2 0.714E-02 0.000E+00
0.10000E+00 0.988E-06 1 4 0.343E-01 0.000E+00
0.10000E+01 0.431E-06 1 5 0.724E-01 0.000E+00
0.10000E+02 0.558E-07 1 3 0.323E+00 0.000E+00
0.10000E+03 0.127E-11 2 1 0.239E+03 0.170E+02
Final statistics for this run:
rwork size = 522 iwork size = 45
number of steps = 105
number of f-s = 225
(excluding J-s) = 207
number of J-s = 3
error overrun = 0.99E+00
Number of errors encountered = 0
==========Source and Output for LSODAR Demonstration Program====================
c-----------------------------------------------------------------------
c Demonstration program for the SLSODAR package.
c This is the version of 12 June 2001.
c
c This version is in single precision.
c
c The SLSODAR package is used to solve two simple problems,
c one nonstiff and one intermittently stiff.
c If the errors are too large, or other difficulty occurs,
c a warning message is printed. All output is on unit lout = 6.
c-----------------------------------------------------------------------
external f1, gr1, f2, jac2, gr2
integer iopt, iout, istate, itask, itol, iwork, jroot, jt,
1 kroot, leniw, lenrw, liw, lrw, lout, neq, nerr, ng,
2 nfe, nfea, nge, nje, nst
real atol, er, ero, errt, rtol, rwork,
1 t, tout, tzero, y, yt
dimension y(2), atol(2), rwork(57), iwork(22), jroot(2)
data lout/6/
c
nerr = 0
c-----------------------------------------------------------------------
c First problem.
c The initial value problem is:
c dy/dt = ((2*log(y) + 8)/t - 5)*y, y(1) = 1, 1 .le. t .le. 6
c The solution is y(t) = exp(-t**2 + 5*t - 4)
c The two root functions are:
c g1 = ((2*log(y)+8)/t - 5)*y (= dy/dt) (with root at t = 2.5),
c g2 = log(y) - 2.2491 (with roots at t = 2.47 and 2.53)
c-----------------------------------------------------------------------
c Set all input parameters and print heading.
neq = 1
y(1) = 1.0e0
t = 1.0e0
tout = 2.0e0
itol = 1
rtol = 1.0e-6
atol(1) = 1.0e-6
itask = 1
istate = 1
iopt = 0
lrw = 44
liw = 21
jt = 2
ng = 2
write (lout,110) itol,rtol,atol(1),jt
110 format(/' Demonstration program for SLSODAR package'////
1 ' First problem'///
2 ' Problem is dy/dt = ((2*log(y)+8)/t - 5)*y, y(1) = 1'//
3 ' Solution is y(t) = exp(-t**2 + 5*t - 4)'//
4 ' Root functions are:'/
5 10x,' g1 = dy/dt (root at t = 2.5)'/
6 10x,' g2 = log(y) - 2.2491 (roots at t = 2.47 and t = 2.53)'//
7 ' itol =',i3,' rtol =',e10.1,' atol =',e10.1//
8 ' jt =',i3///)
c
c Call SLSODAR in loop over tout values 2,3,4,5,6.
ero = 0.0e0
do 180 iout = 1,5
120 continue
call slsodar(f1,neq,y,t,tout,itol,rtol,atol,itask,istate,
1 iopt,rwork,lrw,iwork,liw,jdum,jt,gr1,ng,jroot)
c
c Print y and error in y, and print warning if error too large.
yt = exp(-t*t + 5.0e0*t - 4.0e0)
er = y(1) - yt
write (lout,130) t,y(1),er
130 format(' At t =',e15.7,5x,'y =',e15.7,5x,'error =',e12.4)
if (istate .lt. 0) go to 185
er = abs(er)/(rtol*abs(y(1)) + atol(1))
ero = max(ero,er)
if (er .gt. 1000.0e0) then
write (lout,140)
140 format(//' Warning: error exceeds 1000 * tolerance'//)
nerr = nerr + 1
endif
if (istate .ne. 3) go to 175
c
c If a root was found, write results and check root location.
c Then reset istate to 2 and return to SLSODAR call.
write (lout,150) t,jroot(1),jroot(2)
150 format(/' Root found at t =',e15.7,5x,'jroot =',2i5)
if (jroot(1) .eq. 1) errt = t - 2.5e0
if (jroot(2) .eq. 1 .and. t .le. 2.5e0) errt = t - 2.47e0
if (jroot(2) .eq. 1 .and. t .gt. 2.5e0) errt = t - 2.53e0
write (lout,160) errt
160 format(' Error in t location of root is',e12.4/)
if (abs(errt) .gt. 1.0e-3) then
write (lout,170)
170 format(//' Warning: root error exceeds 1.0e-3'//)
nerr = nerr + 1
endif
istate = 2
go to 120
c
c If no root found, increment tout and loop back.
175 tout = tout + 1.0e0
180 continue
c
c Problem complete. Print final statistics.
185 continue
if (istate .lt. 0) nerr = nerr + 1
nst = iwork(11)
nfe = iwork(12)
nje = iwork(13)
nge = iwork(10)
lenrw = iwork(17)
leniw = iwork(18)
nfea = nfe
if (jt .eq. 2) nfea = nfe - neq*nje
write (lout,190) lenrw,leniw,nst,nfe,nfea,nje,nge,ero
190 format(//' Final statistics for this run:'/
1 ' rwork size =',i4,' iwork size =',i4/
2 ' number of steps =',i5/
3 ' number of f-s =',i5/
4 ' (excluding j-s) =',i5/
5 ' number of j-s =',i5/
6 ' number of g-s =',i5/
7 ' error overrun =',e10.2)
c
c-----------------------------------------------------------------------
c Second problem (Van der Pol oscillator).
c The initial value problem is (after reduction of 2nd order ODE):
c dy1/dt = y2, dy2/dt = 100*(1 - y1**2)*y2 - y1,
c y1(0) = 2, y2(0) = 0, 0 .le. t .le. 200
c The root function is g = y1.
c An analytic solution is not known, but the zeros of y1 are known
c to 15 figures for purposes of checking the accuracy.
c-----------------------------------------------------------------------
c Set tolerance parameters and print heading.
itol = 2
rtol = 1.0e-6
atol(1) = 1.0e-6
atol(2) = 1.0e-4
write (lout,200) itol,rtol,atol(1),atol(2)
200 format(////80('*')//' Second problem (Van der Pol oscillator)'//
1 ' Problem is dy1/dt = y2, dy2/dt = 100*(1-y1**2)*y2 - y1'/
2 ' y1(0) = 2, y2(0) = 0'//
3 ' Root function is g = y1'//
4 ' itol =',i3,' rtol =',e10.1,' atol =',2e10.1)
c
c Loop over jt = 1, 2. Set remaining parameters and print jt.
do 290 jt = 1,2
neq = 2
y(1) = 2.0e0
y(2) = 0.0e0
t = 0.0e0
tout = 20.0e0
itask = 1
istate = 1
iopt = 0
lrw = 57
liw = 22
ng = 1
write (lout,210) jt
210 format(///' Solution with jt =',i2//)
c
c Call SLSODAR in loop over tout values 20,40,...,200.
do 270 iout = 1,10
220 continue
call slsodar(f2,neq,y,t,tout,itol,rtol,atol,itask,istate,
1 iopt,rwork,lrw,iwork,liw,jac2,jt,gr2,ng,jroot)
c
c Print y1 and y2.
write (lout,230) t,y(1),y(2)
230 format(' At t =',e15.7,5x,'y1 =',e15.7,5x,'y2 =',e15.7)
if (istate .lt. 0) go to 275
if (istate .ne. 3) go to 265
c
c If a root was found, write results and check root location.
c Then reset istate to 2 and return to SLSODAR call.
write (lout,240) t
240 format(/' Root found at t =',e15.7)
kroot = int(t/81.2e0 + 0.5e0)
tzero = 81.17237787055e0 + (kroot-1)*81.41853556212e0
errt = t - tzero
write (lout,250) errt
250 format(' Error in t location of root is',e12.4//)
if (abs(errt) .gt. 1.0e-1) then
write (lout,260)
260 format(//' Warning: root error exceeds 1.0e-1'//)
nerr = nerr + 1
endif
istate = 2
go to 220
c
c If no root found, increment tout and loop back.
265 tout = tout + 20.0e0
270 continue
c
c Problem complete. Print final statistics.
275 continue
if (istate .lt. 0) nerr = nerr + 1
nst = iwork(11)
nfe = iwork(12)
nje = iwork(13)
nge = iwork(10)
lenrw = iwork(17)
leniw = iwork(18)
nfea = nfe
if (jt .eq. 2) nfea = nfe - neq*nje
write (lout,280) lenrw,leniw,nst,nfe,nfea,nje,nge
280 format(//' Final statistics for this run:'/
1 ' rwork size =',i4,' iwork size =',i4/
2 ' number of steps =',i5/
3 ' number of f-s =',i5/
4 ' (excluding j-s) =',i5/
5 ' number of j-s =',i5/
6 ' number of g-s =',i5)
290 continue
c
write (lout,300) nerr
300 format(///' Total number of errors encountered =',i3)
stop
end
subroutine f1 (neq, t, y, ydot)
integer neq
real t, y, ydot
dimension y(1), ydot(1)
ydot(1) = ((2.0e0*log(y(1)) + 8.0e0)/t - 5.0e0)*y(1)
return
end
subroutine gr1 (neq, t, y, ng, groot)
integer neq, ng
real t, y, groot
dimension y(1), groot(2)
groot(1) = ((2.0e0*log(y(1)) + 8.0e0)/t - 5.0e0)*y(1)
groot(2) = log(y(1)) - 2.2491e0
return
end
subroutine f2 (neq, t, y, ydot)
integer neq
real t, y, ydot
dimension y(2), ydot(2)
ydot(1) = y(2)
ydot(2) = 100.0e0*(1.0e0 - y(1)*y(1))*y(2) - y(1)
return
end
subroutine jac2 (neq, t, y, ml, mu, pd, nrowpd)
integer neq, ml, mu, nrowpd
real t, y, pd
dimension y(2), pd(nrowpd,2)
pd(1,1) = 0.0e0
pd(1,2) = 1.0e0
pd(2,1) = -200.0e0*y(1)*y(2) - 1.0e0
pd(2,2) = 100.0e0*(1.0e0 - y(1)*y(1))
return
end
subroutine gr2 (neq, t, y, ng, groot)
integer neq, ng
real t, y, groot
dimension y(2), groot(1)
groot(1) = y(1)
return
end
................................................................................
Demonstration program for DLSODAR package
First problem
Problem is dy/dt = ((2*log(y)+8)/t - 5)*y, y(1) = 1
Solution is y(t) = exp(-t**2 + 5*t - 4)
Root functions are:
g1 = dy/dt (root at t = 2.5)
g2 = log(y) - 2.2491 (roots at t = 2.47 and t = 2.53)
itol = 1 rtol = 0.1E-05 atol = 0.1E-05
jt = 2
At t = 0.2000000E+01 y = 0.7389071E+01 error = 0.1534E-04
At t = 0.2469971E+01 y = 0.9479201E+01 error = 0.1631E-04
Root found at t = 0.2469971E+01 jroot = 0 1
Error in t location of root is -0.2865E-04
At t = 0.2500001E+01 y = 0.9487752E+01 error = 0.1613E-04
Root found at t = 0.2500001E+01 jroot = 1 0
Error in t location of root is 0.6800E-06
At t = 0.2530028E+01 y = 0.9479201E+01 error = 0.1601E-04
Root found at t = 0.2530028E+01 jroot = 0 1
Error in t location of root is 0.2813E-04
At t = 0.3000000E+01 y = 0.7389083E+01 error = 0.2667E-04
At t = 0.4000000E+01 y = 0.1000007E+01 error = 0.6703E-05
At t = 0.5000000E+01 y = 0.1831582E-01 error = 0.1814E-06
At t = 0.6000000E+01 y = 0.4536004E-04 error = -0.3989E-07
Final statistics for this run:
rwork size = 42 iwork size = 21
number of steps = 71
number of f-s = 147
(excluding j-s) = 147
number of j-s = 0
number of g-s = 114
error overrun = 0.34E+01
********************************************************************************
Second problem (Van der Pol oscillator)
Problem is dy1/dt = y2, dy2/dt = 100*(1-y1**2)*y2 - y1
y1(0) = 2, y2(0) = 0
Root function is g = y1
itol = 2 rtol = 0.1E-05 atol = 0.1E-05 0.1E-03
Solution with jt = 1
At t = 0.2000000E+02 y1 = 0.1858228E+01 y2 = -0.7575094E-02
At t = 0.4000000E+02 y1 = 0.1693230E+01 y2 = -0.9068584E-02
At t = 0.6000000E+02 y1 = 0.1484608E+01 y2 = -0.1232742E-01
At t = 0.8000000E+02 y1 = 0.1086291E+01 y2 = -0.5840716E-01
At t = 0.8116520E+02 y1 = -0.1308482E-12 y2 = -0.6713980E+02
Root found at t = 0.8116520E+02
Error in t location of root is -0.7180E-02
At t = 0.1000000E+03 y1 = -0.1868862E+01 y2 = 0.7497304E-02
At t = 0.1200000E+03 y1 = -0.1705927E+01 y2 = 0.8930077E-02
At t = 0.1400000E+03 y1 = -0.1501740E+01 y2 = 0.1196163E-01
At t = 0.1600000E+03 y1 = -0.1148800E+01 y2 = 0.3568399E-01
At t = 0.1625761E+03 y1 = 0.1153602E-11 y2 = 0.6713972E+02
Root found at t = 0.1625761E+03
Error in t location of root is -0.1485E-01
At t = 0.1800000E+03 y1 = 0.1879384E+01 y2 = -0.7422067E-02
At t = 0.2000000E+03 y1 = 0.1718431E+01 y2 = -0.8798201E-02
Final statistics for this run:
rwork size = 55 iwork size = 22
number of steps = 478
number of f-s = 931
(excluding j-s) = 931
number of j-s = 42
number of g-s = 513
Solution with jt = 2
At t = 0.2000000E+02 y1 = 0.1858228E+01 y2 = -0.7575094E-02
At t = 0.4000000E+02 y1 = 0.1693230E+01 y2 = -0.9068584E-02
At t = 0.6000000E+02 y1 = 0.1484608E+01 y2 = -0.1232742E-01
At t = 0.8000000E+02 y1 = 0.1086291E+01 y2 = -0.5840716E-01
At t = 0.8116520E+02 y1 = -0.8500767E-12 y2 = -0.6713980E+02
Root found at t = 0.8116520E+02
Error in t location of root is -0.7180E-02
At t = 0.1000000E+03 y1 = -0.1868862E+01 y2 = 0.7497304E-02
At t = 0.1200000E+03 y1 = -0.1705927E+01 y2 = 0.8930077E-02
At t = 0.1400000E+03 y1 = -0.1501740E+01 y2 = 0.1196163E-01
At t = 0.1600000E+03 y1 = -0.1148800E+01 y2 = 0.3568399E-01
At t = 0.1625761E+03 y1 = 0.1057454E-11 y2 = 0.6713972E+02
Root found at t = 0.1625761E+03
Error in t location of root is -0.1485E-01
At t = 0.1800000E+03 y1 = 0.1879384E+01 y2 = -0.7422067E-02
At t = 0.2000000E+03 y1 = 0.1718431E+01 y2 = -0.8798201E-02
Final statistics for this run:
rwork size = 55 iwork size = 22
number of steps = 478
number of f-s = 1015
(excluding j-s) = 931
number of j-s = 42
number of g-s = 516
Total number of errors encountered = 0
==========Source and Output for LSODPK Demonstration Program====================
c-----------------------------------------------------------------------
c Demonstration program for SLSODPK.
c ODE system from ns-species interaction pde in 2 dimensions.
c This is the version of 12 June 2001.
c
c This version is in single precision.
c-----------------------------------------------------------------------
c This program solves a stiff ODE system that arises from a system
c of partial differential equations. The PDE system is a food web
c population model, with predator-prey interaction and diffusion on
c the unit square in two dimensions. The dependent variable vector is
c
c 1 2 ns
c c = (c , c , ..., c )
c
c and the PDEs are as follows:
c
c i i i
c dc /dt = d(i)*(c + c ) + f (x,y,c) (i=1,...,ns)
c xx yy i
c
c where
c i ns j
c f (x,y,c) = c *(b(i) + sum a(i,j)*c )
c i j=1
c
c The number of species is ns = 2*np, with the first np being prey and
c the last np being predators. The coefficients a(i,j), b(i), d(i) are:
c
c a(i,i) = -a (all i)
c a(i,j) = -g (i .le. np, j .gt. np)
c a(i,j) = e (i .gt. np, j .le. np)
c b(i) = b*(1 + alpha*x*y) (i .le. np)
c b(i) = -b*(1 + alpha*x*y) (i .gt. np)
c d(i) = dprey (i .le. np)
c d(i) = dpred (i .gt. np)
c
c The various scalar parameters are set in subroutine setpar.
c
c The boundary conditions are: normal derivative = 0.
c A polynomial in x and y is used to set the initial conditions.
c
c The PDEs are discretized by central differencing on a mx by my mesh.
c
c The ODE system is solved by SLSODPK using method flag values
c mf = 10, 21, 22, 23, 24, 29. The final time is tmax = 10, except
c that for mf = 10 it is tmax = 1.0e-3 because the problem is stiff,
c and for mf = 23 and 24 it is tmax = 2 because the lack of symmetry
c in the problem makes these methods more costly.
c
c Two preconditioner matrices are used. One uses a fixed number of
c Gauss-Seidel iterations based on the diffusion terms only.
c The other preconditioner is a block-diagonal matrix based on
c the partial derivatives of the interaction terms f only, using
c block-grouping (computing only a subset of the ns by ns blocks).
c For mf = 21 and 22, these two preconditioners are applied on
c the left and right, respectively, and for mf = 23 and 24 the product
c of the two is used as the one preconditioner matrix.
c For mf = 29, the inverse of the product is applied.
c
c Two output files are written: one with the problem description and
c and performance statistics on unit 6, and one with solution profiles
c at selected output times (for mf = 22 only) on unit 8.
c-----------------------------------------------------------------------
c Note: In addition to the main program and 10 subroutines
c given below, this program requires the LINPACK subroutines
c SGEFA and SGESL, and the BLAS routine SAXPY.
c-----------------------------------------------------------------------
c Reference:
c Peter N. Brown and Alan C. Hindmarsh,
c Reduced Storage Matrix Methods in Stiff ODE Systems,
c J. Appl. Math. & Comp., 31 (1989), pp. 40-91;
c Also LLNL Report UCRL-95088, Rev. 1, June 1987.
c-----------------------------------------------------------------------
external fweb, jacbg, solsbg
integer ns, mx, my, mxns,
1 mp, mq, mpsq, itmax,
2 meshx,meshy,ngx,ngy,ngrp,mxmp,jgx,jgy,jigx,jigy,jxr,jyr
integer i, imod3, iopt, iout, istate, itask, itol, iwork,
1 jacflg, jpre, leniw, lenrw, liw, lrw, mf,
2 ncfl, ncfn, neq, nfe, nfldif, nfndif, nli, nlidif, nni, nnidif,
3 nout, npe, nps, nqu, nsdif, nst
real aa, ee, gg, bb, dprey, dpred,
1 ax, ay, acoef, bcoef, dx, dy, alph, diff, cox, coy,
2 uround, srur
real avdim, atol, cc, hu, rcfl, rcfn, rumach,
1 rtol, rwork, t, tout
c
c The problem Common blocks below allow for up to 20 species,
c up to a 50x50 mesh, and up to a 20x20 group structure.
common /pcom0/ aa, ee, gg, bb, dprey, dpred
common /pcom1/ ax, ay, acoef(20,20), bcoef(20), dx, dy, alph,
1 diff(20), cox(20), coy(20), ns, mx, my, mxns
common /pcom2/ uround, srur, mp, mq, mpsq, itmax
common /pcom3/ meshx, meshy, ngx, ngy, ngrp, mxmp,
2 jgx(21), jgy(21), jigx(50), jigy(50), jxr(20), jyr(20)
c
c The dimension of cc below must be .ge. 2*neq, where neq = ns*mx*my.
c The dimension lrw of rwork must be .ge. 17*neq + ns*ns*ngrp + 61,
c and the dimension liw of iwork must be .ge. 35 + ns*ngrp.
dimension cc(576), rwork(5213), iwork(67)
data lrw/5213/, liw/67/
c
open (unit=6, file='demout', status='new')
open (unit=8, file='ccout', status='new')
c
ax = 1.0e0
ay = 1.0e0
c
c Call setpar to set problem parameters.
call setpar
c
c Set remaining problem parameters.
neq = ns*mx*my
mxns = mx*ns
dx = ax/(mx-1)
dy = ay/(my-1)
do 10 i = 1,ns
cox(i) = diff(i)/dx**2
10 coy(i) = diff(i)/dy**2
c
c Write heading.
write(6,20)ns, mx,my,neq
20 format(' Demonstration program for SLSODPK package'//
1 ' Food web problem with ns species, ns =',i4/
2 ' Predator-prey interaction and diffusion on a 2-d square'//
3 ' Mesh dimensions (mx,my) =',2i4/
4 ' Total system size is neq =',i7//)
write(6,25) aa,ee,gg,bb,dprey,dpred,alph
25 format(' Matrix parameters: a =',e12.4,' e =',e12.4,
1 ' g =',e12.4/20x,' b =',e12.4//
2 ' Diffusion coefficients: dprey =',e12.4,' dpred =',e12.4/
3 ' Rate parameter alpha =',e12.4//)
c
c Set remaining method parameters.
jpre = 3
jacflg = 1
iwork(3) = jpre
iwork(4) = jacflg
iopt = 0
mp = ns
mq = mx*my
mpsq = ns*ns
uround = rumach()
srur = sqrt(uround)
meshx = mx
meshy = my
mxmp = meshx*mp
ngx = 2
ngy = 2
ngrp = ngx*ngy
call gset (meshx, ngx, jgx, jigx, jxr)
call gset (meshy, ngy, jgy, jigy, jyr)
iwork(1) = mpsq*ngrp
iwork(2) = mp*ngrp
itmax = 5
itol = 1
rtol = 1.0e-5
atol = rtol
itask = 1
write(6,30)ngrp,ngx,ngy,itmax,rtol,atol
30 format(' Preconditioning uses interaction-only block-diagonal',
1 ' matrix'/' with block-grouping, and Gauss-Seidel iterations'//
2 ' Number of diagonal block groups = ngrp =',i4,
3 ' (ngx by ngy, ngx =',i2,' ngy =',i2,' )'//
4 ' G-S preconditioner uses itmax iterations, itmax =',i3//
5 ' Tolerance parameters: rtol =',e10.2,' atol =',e10.2)
c
c
c Loop over mf values 10, 21, ..., 24, 29.
c
do 90 mf = 10,29
if (mf .gt. 10 .and. mf .lt. 21) go to 90
if (mf .gt. 24 .and. mf .lt. 29) go to 90
write(6,40)mf
40 format(//80('-')//' Solution with mf =',i3//
1 ' t nstep nfe nni nli npe nq',
2 4x,'h avdim ncf rate lcf rate')
c
t = 0.0e0
tout = 1.0e-8
nout = 18
if (mf .eq. 10) nout = 6
if (mf .eq. 23 .or. mf .eq. 24) nout = 10
call cinit (cc)
if (mf .eq. 22) call outweb (t, cc, ns, mx, my, 8)
istate = 1
nli = 0
nni = 0
ncfn = 0
ncfl = 0
nst = 0
c
c Loop over output times and call SLSODPK.
c
do 70 iout = 1,nout
call slsodpk (fweb, neq, cc, t, tout, itol, rtol, atol, itask,
1 istate, iopt, rwork, lrw, iwork, liw, jacbg, solsbg, mf)
nsdif = iwork(11) - nst
nst = iwork(11)
nfe = iwork(12)
npe = iwork(13)
nnidif = iwork(19) - nni
nni = iwork(19)
nlidif = iwork(20) - nli
nli = iwork(20)
nfndif = iwork(22) - ncfn
ncfn = iwork(22)
nfldif = iwork(23) - ncfl
ncfl = iwork(23)
nqu = iwork(14)
hu = rwork(11)
avdim = 0.0e0
rcfn = 0.0e0
rcfl = 0.0e0
if (nnidif .gt. 0) avdim = real(nlidif)/real(nnidif)
if (nsdif .gt. 0) rcfn = real(nfndif)/real(nsdif)
if (nnidif .gt. 0) rcfl = real(nfldif)/real(nnidif)
write(6,50)t,nst,nfe,nni,nli,npe,nqu,hu,avdim,rcfn,rcfl
50 format(e10.2,i5,i6,3i5,i4,2e11.2,e10.2,e12.2)
imod3 = iout - 3*(iout/3)
if (mf .eq. 22 .and. imod3 .eq. 0) call outweb (t,cc,ns,mx,my,8)
if (istate .eq. 2) go to 65
write(6,60)t
60 format(//' final time reached =',e12.4//)
go to 75
65 continue
if (tout .gt. 0.9e0) tout = tout + 1.0e0
if (tout .lt. 0.9e0) tout = tout*10.0e0
70 continue
c
75 continue
nst = iwork(11)
nfe = iwork(12)
npe = iwork(13)
lenrw = iwork(17)
leniw = iwork(18)
nni = iwork(19)
nli = iwork(20)
nps = iwork(21)
if (nni .gt. 0) avdim = real(nli)/real(nni)
ncfn = iwork(22)
ncfl = iwork(23)
write (6,80) lenrw,leniw,nst,nfe,npe,nps,nni,nli,avdim,
1 ncfn,ncfl
80 format(//' Final statistics for this run:'/
1 ' rwork size =',i8,' iwork size =',i6/
2 ' number of time steps =',i5/
3 ' number of f evaluations =',i5/
4 ' number of preconditioner evals. =',i5/
4 ' number of preconditioner solves =',i5/
5 ' number of nonlinear iterations =',i5/
5 ' number of linear iterations =',i5/
6 ' average subspace dimension =',f8.4/
7 i5,' nonlinear conv. failures,',i5,' linear conv. failures')
c
90 continue
stop
c------ end of main program for SLSODPK demonstration program ----------
end
subroutine setpar
c-----------------------------------------------------------------------
c This routine sets the problem parameters.
c It set ns, mx, my, and problem coefficients acoef, bcoef, diff, alph,
c using parameters np, aa, ee, gg, bb, dprey, dpred.
c-----------------------------------------------------------------------
integer ns, mx, my, mxns
integer i, j, np
real aa, ee, gg, bb, dprey, dpred,
1 ax, ay, acoef, bcoef, dx, dy, alph, diff, cox, coy
common /pcom0/ aa, ee, gg, bb, dprey, dpred
common /pcom1/ ax, ay, acoef(20,20), bcoef(20), dx, dy, alph,
1 diff(20), cox(20), coy(20), ns, mx, my, mxns
c
np = 3
mx = 6
my = 6
aa = 1.0e0
ee = 1.0e4
gg = 0.5e-6
bb = 1.0e0
dprey = 1.0e0
dpred = 0.5e0
alph = 1.0e0
ns = 2*np
do 70 j = 1,np
do 60 i = 1,np
acoef(np+i,j) = ee
acoef(i,np+j) = -gg
60 continue
acoef(j,j) = -aa
acoef(np+j,np+j) = -aa
bcoef(j) = bb
bcoef(np+j) = -bb
diff(j) = dprey
diff(np+j) = dpred
70 continue
c
return
c------------ end of subroutine setpar -------------------------------
end
subroutine gset (m, ng, jg, jig, jr)
c-----------------------------------------------------------------------
c This routine sets arrays jg, jig, and jr describing
c a uniform partition of (1,2,...,m) into ng groups.
c-----------------------------------------------------------------------
integer m, ng, jg, jig, jr
dimension jg(*), jig(*), jr(*)
integer ig, j, len1, mper, ngm1
c
mper = m/ng
do 10 ig = 1,ng
10 jg(ig) = 1 + (ig - 1)*mper
jg(ng+1) = m + 1
c
ngm1 = ng - 1
len1 = ngm1*mper
do 20 j = 1,len1
20 jig(j) = 1 + (j-1)/mper
len1 = len1 + 1
do 25 j = len1,m
25 jig(j) = ng
c
do 30 ig = 1,ngm1
30 jr(ig) = 0.5e0 + (ig - 0.5e0)*mper
jr(ng) = 0.5e0*(1 + ngm1*mper + m)
c
return
c------------ end of subroutine gset ---------------------------------
end
subroutine cinit (cc)
c-----------------------------------------------------------------------
c This routine computes and loads the vector of initial values.
c-----------------------------------------------------------------------
real cc
dimension cc(*)
integer ns, mx, my, mxns
integer i, ici, ioff, iyoff, jx, jy
real ax,ay,acoef,bcoef,dx,dy,alph,diff,cox,coy
real argx, argy, x, y
common /pcom1/ ax, ay, acoef(20,20), bcoef(20), dx, dy, alph,
1 diff(20), cox(20), coy(20), ns, mx, my, mxns
c
do 20 jy = 1,my
y = (jy-1)*dy
argy = 16.0e0*y*y*(ay-y)*(ay-y)
iyoff = mxns*(jy-1)
do 10 jx = 1,mx
x = (jx-1)*dx
argx = 16.0e0*x*x*(ax-x)*(ax-x)
ioff = iyoff + ns*(jx-1)
do 5 i = 1,ns
ici = ioff + i
cc(ici) = 10.0e0 + i*argx*argy
5 continue
10 continue
20 continue
return
c------------ end of subroutine cinit --------------------------------
end
subroutine outweb (t, c, ns, mx, my, lun)
c-----------------------------------------------------------------------
c This routine prints the values of the individual species densities
c at the current time t. The write statements use unit lun.
c-----------------------------------------------------------------------
integer ns, mx, my, lun
real t, c
dimension c(ns,mx,my)
integer i, jx, jy
c
write(lun,10) t
10 format(/80('-')/30x,'At time t = ',e16.8/80('-') )
c
do 40 i = 1,ns
write(lun,20) i
20 format(' the species c(',i2,') values are:')
do 30 jy = my,1,-1
write(lun,25) (c(i,jx,jy),jx=1,mx)
25 format(6(1x,g12.6))
30 continue
write(lun,35)
35 format(80('-'),/)
40 continue
c
return
c------------ end of subroutine outweb -------------------------------
end
subroutine fweb (neq, t, cc, cdot)
c-----------------------------------------------------------------------
c This routine computes the derivative of cc and returns it in cdot.
c The interaction rates are computed by calls to webr, and these are
c saved in cc(neq+1),...,cc(2*neq) for use in preconditioning.
c-----------------------------------------------------------------------
integer neq
real t, cc, cdot
dimension cc(neq), cdot(neq)
integer ns, mx, my, mxns
integer i, ic, ici, idxl, idxu, idyl, idyu, iyoff, jx, jy
real ax,ay,acoef,bcoef,dx,dy,alph,diff,cox,coy
real dcxli, dcxui, dcyli, dcyui, x, y
common /pcom1/ ax, ay, acoef(20,20), bcoef(20), dx, dy, alph,
1 diff(20), cox(20), coy(20), ns, mx, my, mxns
c
do 100 jy = 1,my
y = (jy-1)*dy
iyoff = mxns*(jy-1)
idyu = mxns
if (jy .eq. my) idyu = -mxns
idyl = mxns
if (jy .eq. 1) idyl = -mxns
do 90 jx = 1,mx
x = (jx-1)*dx
ic = iyoff + ns*(jx-1) + 1
c Get interaction rates at one point (x,y).
call webr (x, y, t, cc(ic), cc(neq+ic))
idxu = ns
if (jx .eq. mx) idxu = -ns
idxl = ns
if (jx .eq. 1) idxl = -ns
do 80 i = 1,ns
ici = ic + i - 1
c Do differencing in y.
dcyli = cc(ici) - cc(ici-idyl)
dcyui = cc(ici+idyu) - cc(ici)
c Do differencing in x.
dcxli = cc(ici) - cc(ici-idxl)
dcxui = cc(ici+idxu) - cc(ici)
c Collect terms and load cdot elements.
cdot(ici) = coy(i)*(dcyui - dcyli) + cox(i)*(dcxui - dcxli)
1 + cc(neq+ici)
80 continue
90 continue
100 continue
return
c------------ end of subroutine fweb ---------------------------------
end
subroutine webr (x, y, t, c, rate)
c-----------------------------------------------------------------------
c This routine computes the interaction rates for the species
c c(1),...,c(ns), at one spatial point and at time t.
c-----------------------------------------------------------------------
real x, y, t, c, rate
dimension c(*), rate(*)
integer ns, mx, my, mxns
integer i
real ax,ay,acoef,bcoef,dx,dy,alph,diff,cox,coy
real fac
common /pcom1/ ax, ay, acoef(20,20), bcoef(20), dx, dy, alph,
1 diff(20), cox(20), coy(20), ns, mx, my, mxns
c
do 10 i = 1,ns
10 rate(i) = 0.0e0
do 15 i = 1,ns
call saxpy (ns, c(i), acoef(1,i), 1, rate, 1)
15 continue
fac = 1.0e0 + alph*x*y
do 20 i = 1,ns
20 rate(i) = c(i)*(bcoef(i)*fac + rate(i))
return
c------------ end of subroutine webr ---------------------------------
end
subroutine jacbg (f, neq, t, cc, ccsv, rewt, f0, f1, hl0,
1 bd, ipbd, ier)
c-----------------------------------------------------------------------
c This routine generates part of the block-diagonal part of the
c Jacobian, multiplies by -hl0, adds the identity matrix,
c and calls SGEFA to do LU decomposition of each diagonal block.
c The computation of the diagonal blocks uses the block and grouping
c information in /pcom1/ and /pcom2/. One block per group is computed.
c The Jacobian elements are generated by difference quotients
c using calls to the routine fbg.
c-----------------------------------------------------------------------
c The two Common blocks below are used for internal communication.
c The variables used are:
c mp = size of blocks in block-diagonal preconditioning matrix.
c mq = number of blocks in each direction (neq = mp*mq).
c mpsq = mp*mp.
c uround = unit roundoff, generated by a call uround = rumach().
c srur = sqrt(uround).
c meshx = x mesh size
c meshy = y mesh size (mesh is meshx by meshy)
c ngx = no. groups in x direction in block-grouping scheme.
c ngy = no. groups in y direction in block-grouping scheme.
c ngrp = total number of groups = ngx*ngy.
c mxmp = meshx*mp.
c jgx = length ngx+1 array of group boundaries in x direction.
c group igx has x indices jx = jgx(igx),...,jgx(igx+1)-1.
c jigx = length meshx array of x group indices vs x node index.
c x node index jx is in x group jigx(jx).
c jxr = length ngx array of x indices representing the x groups.
c the index for x group igx is jx = jxr(igx).
c jgy, jigy, jyr = analogous arrays for grouping in y direction.
c-----------------------------------------------------------------------
external f
integer neq, ipbd, ier
real t, cc, ccsv, rewt, f0, f1, hl0, bd
dimension cc(neq), ccsv(neq), rewt(neq), f0(neq), f1(neq),
1 bd(*), ipbd(*)
integer mp, mq, mpsq, itmax,
2 meshx,meshy,ngx,ngy,ngrp,mxmp,jgx,jgy,jigx,jigy,jxr,jyr
integer i, ibd, idiag, if0, if00, ig, igx, igy, iip,
1 j, jj, jx, jy, n
real uround, srur
real fac, r, r0, svnorm
c
common /pcom2/ uround, srur, mp, mq, mpsq, itmax
common /pcom3/ meshx, meshy, ngx, ngy, ngrp, mxmp,
1 jgx(21), jgy(21), jigx(50), jigy(50), jxr(20), jyr(20)
c
n = neq
c
c-----------------------------------------------------------------------
c Make mp calls to fbg to approximate each diagonal block of Jacobian.
c Here cc(neq+1),...,cc(2*neq) contains the base fb value.
c r0 is a minimum increment factor for the difference quotient.
c-----------------------------------------------------------------------
200 fac = svnorm (n, f0, rewt)
r0 = 1000.0e0*abs(hl0)*uround*n*fac
if (r0 .eq. 0.0e0) r0 = 1.0e0
ibd = 0
do 240 igy = 1,ngy
jy = jyr(igy)
if00 = (jy - 1)*mxmp
do 230 igx = 1,ngx
jx = jxr(igx)
if0 = if00 + (jx - 1)*mp
do 220 j = 1,mp
jj = if0 + j
r = max(srur*abs(cc(jj)),r0/rewt(jj))
cc(jj) = cc(jj) + r
fac = -hl0/r
call fbg (neq, t, cc, jx, jy, f1)
do 210 i = 1,mp
210 bd(ibd+i) = (f1(i) - cc(neq+if0+i))*fac
cc(jj) = ccsv(jj)
ibd = ibd + mp
220 continue
230 continue
240 continue
c
c Add identity matrix and do LU decompositions on blocks. --------------
260 continue
ibd = 1
iip = 1
do 280 ig = 1,ngrp
idiag = ibd
do 270 i = 1,mp
bd(idiag) = bd(idiag) + 1.0e0
270 idiag = idiag + (mp + 1)
call sgefa (bd(ibd), mp, mp, ipbd(iip), ier)
if (ier .ne. 0) go to 290
ibd = ibd + mpsq
iip = iip + mp
280 continue
290 return
c------------ end of subroutine jacbg --------------------------------
end
subroutine fbg (neq, t, cc, jx, jy, cdot)
c-----------------------------------------------------------------------
c This routine computes one block of the interaction terms of the
c system, namely block (jx,jy), for use in preconditioning.
c-----------------------------------------------------------------------
integer neq, jx, jy
real t, cc, cdot
dimension cc(neq), cdot(neq)
integer ns, mx, my, mxns
integer iblok, ic
real ax,ay,acoef,bcoef,dx,dy,alph,diff,cox,coy
real x, y
c
common /pcom1/ ax, ay, acoef(20,20), bcoef(20), dx, dy, alph,
1 diff(20), cox(20), coy(20), ns, mx, my, mxns
c
iblok = jx + (jy-1)*mx
y = (jy-1)*dy
x = (jx-1)*dx
ic = ns*(iblok-1) + 1
call webr (x, y, t, cc(ic), cdot)
return
c------------ end of subroutine fbg ----------------------------------
end
subroutine solsbg (n, t, cc, f0, wk, hl0, bd, ipbd, v, lr, ier)
c-----------------------------------------------------------------------
c This routine applies one or two inverse preconditioner matrices
c to the array v, using the interaction-only block-diagonal Jacobian
c with block-grouping, and Gauss-Seidel applied to the diffusion terms.
c When lr = 1 or 3, it calls gs for a Gauss-Seidel approximation
c to ((I-hl0*Jd)-inverse)*v, and stores the result in v.
c When lr = 2 or 3, it computes ((I-hl0*dg/dc)-inverse)*v, using LU
c factors of the blocks in bd, and pivot information in ipbd.
c In both cases, the array v is overwritten with the solution.
c-----------------------------------------------------------------------
integer n, ipbd, lr, ier
real t, cc, f0, wk, hl0, bd, v
dimension cc(n), f0(n), wk(n), bd(*), ipbd(*), v(n)
integer mp, mq, mpsq, itmax,
2 meshx,meshy,ngx,ngy,ngrp,mxmp,jgx,jgy,jigx,jigy,jxr,jyr
integer ibd, ig0, igm1, igx, igy, iip, iv, jx, jy
real uround, srur
c
common /pcom2/ uround, srur, mp, mq, mpsq, itmax
common /pcom3/ meshx, meshy, ngx, ngy, ngrp, mxmp,
1 jgx(21), jgy(21), jigx(50), jigy(50), jxr(20), jyr(20)
c
ier = 0
c
if (lr.eq.0 .or. lr.eq.1 .or. lr.eq.3) call gs (n, hl0, v, wk)
if (lr.eq.0 .or. lr.eq.2 .or. lr.eq.3) then
iv = 1
do 20 jy = 1,meshy
igy = jigy(jy)
ig0 = (igy - 1)*ngx
do 10 jx = 1,meshx
igx = jigx(jx)
igm1 = igx - 1 + ig0
ibd = 1 + igm1*mpsq
iip = 1 + igm1*mp
call sgesl (bd(ibd), mp, mp, ipbd(iip), v(iv), 0)
iv = iv + mp
10 continue
20 continue
endif
c
return
c------------ end of subroutine solsbg -------------------------------
end
subroutine gs (n, hl0, z, x)
c-----------------------------------------------------------------------
c This routine performs itmax Gauss-Seidel iterations
c to compute an approximation to P-inverse*z, where P = I - hl0*Jd, and
c Jd represents the diffusion contributions to the Jacobian.
c z contains the answer on return.
c The dimensions below assume ns .le. 20.
c-----------------------------------------------------------------------
integer n
real hl0, z, x
dimension z(n), x(n)
integer ns, mx, my, mxns,
1 mp, mq, mpsq, itmax
integer i, ic, ici, iter, iyoff, jx, jy
real ax,ay,acoef,bcoef,dx,dy,alph,diff,cox,coy,
2 uround, srur
real beta,beta2,cof1,elamda,gamma,gamma2
dimension beta(20), gamma(20), beta2(20), gamma2(20), cof1(20)
common /pcom1/ ax, ay, acoef(20,20), bcoef(20), dx, dy, alph,
1 diff(20), cox(20), coy(20), ns, mx, my, mxns
common /pcom2/ uround, srur, mp, mq, mpsq, itmax
c
c-----------------------------------------------------------------------
c Write matrix as P = D - L - U.
c Load local arrays beta, beta2, gamma, gamma2, and cof1.
c-----------------------------------------------------------------------
do 10 i = 1,ns
elamda = 1.e0/(1.e0 + 2.e0*hl0*(cox(i) + coy(i)))
beta(i) = hl0*cox(i)*elamda
beta2(i) = 2.e0*beta(i)
gamma(i) = hl0*coy(i)*elamda
gamma2(i) = 2.e0*gamma(i)
cof1(i) = elamda
10 continue
c-----------------------------------------------------------------------
c Begin iteration loop.
c Load array x with (D-inverse)*z for first iteration.
c-----------------------------------------------------------------------
iter = 1
c
do 50 jy = 1,my
iyoff = mxns*(jy-1)
do 40 jx = 1,mx
ic = iyoff + ns*(jx-1)
do 30 i = 1,ns
ici = ic + i
x(ici) = cof1(i)*z(ici)
z(ici) = 0.e0
30 continue
40 continue
50 continue
go to 160
c-----------------------------------------------------------------------
c Calculate (D-inverse)*U*x.
c-----------------------------------------------------------------------
70 continue
iter = iter + 1
jy = 1
jx = 1
ic = ns*(jx-1)
do 75 i = 1,ns
ici = ic + i
75 x(ici) = beta2(i)*x(ici+ns) + gamma2(i)*x(ici+mxns)
do 85 jx = 2,mx-1
ic = ns*(jx-1)
do 80 i = 1,ns
ici = ic + i
80 x(ici) = beta(i)*x(ici+ns) + gamma2(i)*x(ici+mxns)
85 continue
jx = mx
ic = ns*(jx-1)
do 90 i = 1,ns
ici = ic + i
90 x(ici) = gamma2(i)*x(ici+mxns)
do 115 jy = 2,my-1
iyoff = mxns*(jy-1)
jx = 1
ic = iyoff
do 95 i = 1,ns
ici = ic + i
95 x(ici) = beta2(i)*x(ici+ns) + gamma(i)*x(ici+mxns)
do 105 jx = 2,mx-1
ic = iyoff + ns*(jx-1)
do 100 i = 1,ns
ici = ic + i
100 x(ici) = beta(i)*x(ici+ns) + gamma(i)*x(ici+mxns)
105 continue
jx = mx
ic = iyoff + ns*(jx-1)
do 110 i = 1,ns
ici = ic + i
110 x(ici) = gamma(i)*x(ici+mxns)
115 continue
jy = my
iyoff = mxns*(jy-1)
jx = 1
ic = iyoff
do 120 i = 1,ns
ici = ic + i
120 x(ici) = beta2(i)*x(ici+ns)
do 130 jx = 2,mx-1
ic = iyoff + ns*(jx-1)
do 125 i = 1,ns
ici = ic + i
125 x(ici) = beta(i)*x(ici+ns)
130 continue
jx = mx
ic = iyoff + ns*(jx-1)
do 135 i = 1,ns
ici = ic + i
135 x(ici) = 0.0e0
c-----------------------------------------------------------------------
c Calculate (I - (D-inverse)*L)*x.
c-----------------------------------------------------------------------
160 continue
jy = 1
do 175 jx = 2,mx-1
ic = ns*(jx-1)
do 170 i = 1,ns
ici = ic + i
170 x(ici) = x(ici) + beta(i)*x(ici-ns)
175 continue
jx = mx
ic = ns*(jx-1)
do 180 i = 1,ns
ici = ic + i
180 x(ici) = x(ici) + beta2(i)*x(ici-ns)
do 210 jy = 2,my-1
iyoff = mxns*(jy-1)
jx = 1
ic = iyoff
do 185 i = 1,ns
ici = ic + i
185 x(ici) = x(ici) + gamma(i)*x(ici-mxns)
do 200 jx = 2,mx-1
ic = iyoff + ns*(jx-1)
do 195 i = 1,ns
ici = ic + i
x(ici) = (x(ici) + beta(i)*x(ici-ns))
1 + gamma(i)*x(ici-mxns)
195 continue
200 continue
jx = mx
ic = iyoff + ns*(jx-1)
do 205 i = 1,ns
ici = ic + i
x(ici) = (x(ici) + beta2(i)*x(ici-ns))
1 + gamma(i)*x(ici-mxns)
205 continue
210 continue
jy = my
iyoff = mxns*(jy-1)
jx = 1
ic = iyoff
do 215 i = 1,ns
ici = ic + i
215 x(ici) = x(ici) + gamma2(i)*x(ici-mxns)
do 225 jx = 2,mx-1
ic = iyoff + ns*(jx-1)
do 220 i = 1,ns
ici = ic + i
x(ici) = (x(ici) + beta(i)*x(ici-ns))
1 + gamma2(i)*x(ici-mxns)
220 continue
225 continue
jx = mx
ic = iyoff + ns*(jx-1)
do 230 i = 1,ns
ici = ic + i
x(ici) = (x(ici) + beta2(i)*x(ici-ns))
1 + gamma2(i)*x(ici-mxns)
230 continue
c-----------------------------------------------------------------------
c Add increment x to z.
c-----------------------------------------------------------------------
do 300 i = 1,n
300 z(i) = z(i) + x(i)
c
if (iter .lt. itmax) go to 70
return
c------------ end of subroutine gs -----------------------------------
end
................................................................................
Demonstration program for DLSODPK package
Food web problem with ns species, ns = 6
Predator-prey interaction and diffusion on a 2-d square
Mesh dimensions (mx,my) = 6 6
Total system size is neq = 216
Matrix parameters: a = 0.1000E+01 e = 0.1000E+05 g = 0.5000E-06
b = 0.1000E+01
Diffusion coefficients: dprey = 0.1000E+01 dpred = 0.5000E+00
Rate parameter alpha = 0.1000E+01
Preconditioning uses interaction-only block-diagonal matrix
with block-grouping, and Gauss-Seidel iterations
Number of diagonal block groups = ngrp = 4 (ngx by ngy, ngx = 2 ngy = 2 )
G-S preconditioner uses itmax iterations, itmax = 5
Tolerance parameters: rtol = 0.10E-04 atol = 0.10E-04
--------------------------------------------------------------------------------
Solution with mf = 10
t nstep nfe nni nli npe nq h avdim ncf rate lcf rate
0.10E-07 3 4 0 0 0 2 0.10E-06 0.00E+00 0.00E+00 0.00E+00
0.10E-06 3 4 0 0 0 2 0.10E-06 0.00E+00 0.00E+00 0.00E+00
0.10E-05 7 13 0 0 0 3 0.35E-06 0.00E+00 0.00E+00 0.00E+00
0.10E-04 22 41 0 0 0 6 0.10E-05 0.00E+00 0.00E+00 0.00E+00
0.10E-03 81 155 0 0 0 2 0.24E-05 0.00E+00 0.34E-01 0.00E+00
0.10E-02 397 899 0 0 0 2 0.43E-05 0.00E+00 0.22E+00 0.00E+00
Final statistics for this run:
rwork size = 3476 iwork size = 30
number of time steps = 397
number of f evaluations = 899
number of preconditioner evals. = 0
number of preconditioner solves = 0
number of nonlinear iterations = 0
number of linear iterations = 0
average subspace dimension = 0.0000
73 nonlinear conv. failures, 0 linear conv. failures
--------------------------------------------------------------------------------
Solution with mf = 21
t nstep nfe nni nli npe nq h avdim ncf rate lcf rate
0.10E-07 3 5 3 1 2 2 0.65E-07 0.33E+00 0.00E+00 0.00E+00
0.10E-06 4 8 5 2 2 2 0.65E-07 0.50E+00 0.00E+00 0.00E+00
0.10E-05 10 22 13 8 4 3 0.37E-06 0.75E+00 0.00E+00 0.00E+00
0.10E-04 33 78 43 34 6 5 0.51E-06 0.87E+00 0.00E+00 0.00E+00
0.10E-03 112 270 134 135 14 5 0.60E-05 0.11E+01 0.00E+00 0.00E+00
0.10E-02 131 321 156 164 18 2 0.35E-03 0.13E+01 0.00E+00 0.00E+00
0.10E-01 138 343 167 175 20 3 0.18E-02 0.10E+01 0.00E+00 0.00E+00
0.10E+00 162 402 194 207 23 4 0.71E-02 0.12E+01 0.00E+00 0.00E+00
0.10E+01 206 540 242 297 27 4 0.47E-01 0.19E+01 0.00E+00 0.00E+00
0.20E+01 221 608 259 348 29 4 0.96E-01 0.30E+01 0.00E+00 0.00E+00
0.30E+01 230 656 269 386 30 4 0.16E+00 0.38E+01 0.00E+00 0.00E+00
0.40E+01 236 694 276 417 31 4 0.21E+00 0.44E+01 0.00E+00 0.29E+00
0.50E+01 240 718 280 437 31 4 0.27E+00 0.50E+01 0.00E+00 0.75E+00
0.60E+01 244 742 284 457 31 4 0.27E+00 0.50E+01 0.00E+00 0.75E+00
0.70E+01 247 766 288 477 32 4 0.36E+00 0.50E+01 0.00E+00 0.10E+01
0.80E+01 250 790 292 497 33 4 0.48E+00 0.50E+01 0.00E+00 0.10E+01
0.90E+01 252 802 294 507 33 4 0.48E+00 0.50E+01 0.00E+00 0.10E+01
0.10E+02 254 814 296 517 33 4 0.48E+00 0.50E+01 0.00E+00 0.10E+01
Final statistics for this run:
rwork size = 3861 iwork size = 59
number of time steps = 254
number of f evaluations = 814
number of preconditioner evals. = 33
number of preconditioner solves = 1554
number of nonlinear iterations = 296
number of linear iterations = 517
average subspace dimension = 1.7466
0 nonlinear conv. failures, 20 linear conv. failures
--------------------------------------------------------------------------------
Solution with mf = 22
t nstep nfe nni nli npe nq h avdim ncf rate lcf rate
0.10E-07 3 5 3 1 2 2 0.65E-07 0.33E+00 0.00E+00 0.00E+00
0.10E-06 4 8 5 2 2 2 0.65E-07 0.50E+00 0.00E+00 0.00E+00
0.10E-05 10 22 13 8 4 3 0.37E-06 0.75E+00 0.00E+00 0.00E+00
0.10E-04 33 78 43 34 6 5 0.51E-06 0.87E+00 0.00E+00 0.00E+00
0.10E-03 112 270 134 135 14 5 0.60E-05 0.11E+01 0.00E+00 0.00E+00
0.10E-02 131 321 156 164 18 2 0.35E-03 0.13E+01 0.00E+00 0.00E+00
0.10E-01 138 343 167 175 20 3 0.18E-02 0.10E+01 0.00E+00 0.00E+00
0.10E+00 162 402 194 207 23 4 0.71E-02 0.12E+01 0.00E+00 0.00E+00
0.10E+01 206 543 242 300 27 4 0.47E-01 0.19E+01 0.00E+00 0.00E+00
0.20E+01 221 612 259 352 29 4 0.95E-01 0.31E+01 0.00E+00 0.00E+00
0.30E+01 230 661 269 391 30 4 0.16E+00 0.39E+01 0.00E+00 0.10E+00
0.40E+01 236 695 275 419 30 4 0.20E+00 0.47E+01 0.00E+00 0.67E+00
0.50E+01 241 731 281 449 31 4 0.27E+00 0.50E+01 0.00E+00 0.10E+01
0.60E+01 244 749 284 464 31 4 0.27E+00 0.50E+01 0.00E+00 0.10E+01
0.70E+01 247 773 288 484 32 4 0.36E+00 0.50E+01 0.00E+00 0.10E+01
0.80E+01 250 797 292 504 33 3 0.51E+00 0.50E+01 0.00E+00 0.10E+01
0.90E+01 252 809 294 514 33 3 0.51E+00 0.50E+01 0.00E+00 0.10E+01
0.10E+02 254 827 297 529 34 2 0.82E+00 0.50E+01 0.00E+00 0.10E+01
Final statistics for this run:
rwork size = 3877 iwork size = 54
number of time steps = 254
number of f evaluations = 827
number of preconditioner evals. = 34
number of preconditioner solves = 1580
number of nonlinear iterations = 297
number of linear iterations = 529
average subspace dimension = 1.7811
0 nonlinear conv. failures, 27 linear conv. failures
--------------------------------------------------------------------------------
Solution with mf = 23
t nstep nfe nni nli npe nq h avdim ncf rate lcf rate
0.10E-07 3 5 3 1 2 2 0.65E-07 0.33E+00 0.00E+00 0.00E+00
0.10E-06 4 8 5 2 2 2 0.65E-07 0.50E+00 0.00E+00 0.00E+00
0.10E-05 10 22 13 8 4 3 0.37E-06 0.75E+00 0.00E+00 0.00E+00
0.10E-04 33 78 43 34 6 5 0.51E-06 0.87E+00 0.00E+00 0.00E+00
0.10E-03 112 272 134 137 14 5 0.60E-05 0.11E+01 0.00E+00 0.00E+00
0.10E-02 131 324 156 167 18 2 0.35E-03 0.14E+01 0.00E+00 0.00E+00
0.10E-01 139 360 166 193 20 3 0.15E-02 0.26E+01 0.00E+00 0.40E+00
0.10E+00 172 503 209 293 28 4 0.53E-02 0.23E+01 0.91E-01 0.26E+00
0.10E+01 227 845 278 566 42 4 0.11E-01 0.40E+01 0.91E-01 0.52E+00
0.20E+01 280 1287 360 926 70 2 0.17E-01 0.44E+01 0.25E+00 0.76E+00
Final statistics for this run:
rwork size = 3404 iwork size = 54
number of time steps = 280
number of f evaluations = 1287
number of preconditioner evals. = 70
number of preconditioner solves = 926
number of nonlinear iterations = 360
number of linear iterations = 926
average subspace dimension = 2.5722
21 nonlinear conv. failures, 113 linear conv. failures
--------------------------------------------------------------------------------
Solution with mf = 24
t nstep nfe nni nli npe nq h avdim ncf rate lcf rate
0.10E-07 3 5 3 1 2 2 0.65E-07 0.33E+00 0.00E+00 0.00E+00
0.10E-06 4 8 5 2 2 2 0.65E-07 0.50E+00 0.00E+00 0.00E+00
0.10E-05 10 22 13 8 4 3 0.37E-06 0.75E+00 0.00E+00 0.00E+00
0.10E-04 33 78 43 34 6 5 0.51E-06 0.87E+00 0.00E+00 0.00E+00
0.10E-03 112 270 134 135 14 5 0.60E-05 0.11E+01 0.00E+00 0.00E+00
0.10E-02 131 321 156 164 18 2 0.35E-03 0.13E+01 0.00E+00 0.00E+00
0.10E-01 139 356 167 188 20 3 0.16E-02 0.22E+01 0.00E+00 0.27E+00
0.10E+00 162 412 193 218 23 4 0.71E-02 0.12E+01 0.00E+00 0.00E+00
0.10E+01 223 780 274 505 38 4 0.23E-01 0.35E+01 0.82E-01 0.43E+00
0.20E+01 263 1085 335 749 59 3 0.17E-01 0.40E+01 0.23E+00 0.56E+00
Final statistics for this run:
rwork size = 3404 iwork size = 54
number of time steps = 263
number of f evaluations = 1085
number of preconditioner evals. = 59
number of preconditioner solves = 749
number of nonlinear iterations = 335
number of linear iterations = 749
average subspace dimension = 2.2358
14 nonlinear conv. failures, 72 linear conv. failures
--------------------------------------------------------------------------------
Solution with mf = 29
t nstep nfe nni nli npe nq h avdim ncf rate lcf rate
0.10E-07 3 4 3 0 2 2 0.65E-07 0.00E+00 0.00E+00 0.00E+00
0.10E-06 4 6 5 0 2 2 0.65E-07 0.00E+00 0.00E+00 0.00E+00
0.10E-05 10 14 13 0 4 3 0.37E-06 0.00E+00 0.00E+00 0.00E+00
0.10E-04 32 42 41 0 6 5 0.56E-06 0.00E+00 0.00E+00 0.00E+00
0.10E-03 114 135 134 0 13 5 0.47E-05 0.00E+00 0.00E+00 0.00E+00
0.10E-02 136 162 161 0 18 2 0.30E-03 0.00E+00 0.00E+00 0.00E+00
0.10E-01 144 173 172 0 20 3 0.16E-02 0.00E+00 0.00E+00 0.00E+00
0.10E+00 168 200 199 0 23 4 0.79E-02 0.00E+00 0.00E+00 0.00E+00
0.10E+01 245 353 352 0 39 2 0.17E-01 0.00E+00 0.13E-01 0.00E+00
0.20E+01 293 467 466 0 57 2 0.28E-01 0.00E+00 0.10E+00 0.00E+00
0.30E+01 330 566 565 0 76 2 0.37E-01 0.00E+00 0.22E+00 0.00E+00
0.40E+01 356 631 630 0 87 2 0.31E-01 0.00E+00 0.15E+00 0.00E+00
0.50E+01 384 697 696 0 98 1 0.72E-01 0.00E+00 0.14E+00 0.00E+00
0.60E+01 399 742 741 0 109 2 0.21E+00 0.00E+00 0.27E+00 0.00E+00
0.70E+01 411 783 782 0 117 1 0.20E+00 0.00E+00 0.33E+00 0.00E+00
0.80E+01 414 788 787 0 118 2 0.41E+00 0.00E+00 0.00E+00 0.00E+00
0.90E+01 416 791 790 0 118 2 0.41E+00 0.00E+00 0.00E+00 0.00E+00
0.10E+02 418 793 792 0 119 3 0.74E+00 0.00E+00 0.00E+00 0.00E+00
Final statistics for this run:
rwork size = 2756 iwork size = 54
number of time steps = 418
number of f evaluations = 793
number of preconditioner evals. = 119
number of preconditioner solves = 777
number of nonlinear iterations = 792
number of linear iterations = 0
average subspace dimension = 0.0000
30 nonlinear conv. failures, 0 linear conv. failures
................................................................................
--------------------------------------------------------------------------------
At time t = 0.00000000E+00
--------------------------------------------------------------------------------
the species c( 1) values are:
10.0000 10.0000 10.0000 10.0000 10.0000 10.0000
10.0000 10.1678 10.3775 10.3775 10.1678 10.0000
10.0000 10.3775 10.8493 10.8493 10.3775 10.0000
10.0000 10.3775 10.8493 10.8493 10.3775 10.0000
10.0000 10.1678 10.3775 10.3775 10.1678 10.0000
10.0000 10.0000 10.0000 10.0000 10.0000 10.0000
--------------------------------------------------------------------------------
the species c( 2) values are:
10.0000 10.0000 10.0000 10.0000 10.0000 10.0000
10.0000 10.3355 10.7550 10.7550 10.3355 10.0000
10.0000 10.7550 11.6987 11.6987 10.7550 10.0000
10.0000 10.7550 11.6987 11.6987 10.7550 10.0000
10.0000 10.3355 10.7550 10.7550 10.3355 10.0000
10.0000 10.0000 10.0000 10.0000 10.0000 10.0000
--------------------------------------------------------------------------------
the species c( 3) values are:
10.0000 10.0000 10.0000 10.0000 10.0000 10.0000
10.0000 10.5033 11.1325 11.1325 10.5033 10.0000
10.0000 11.1325 12.5480 12.5480 11.1325 10.0000
10.0000 11.1325 12.5480 12.5480 11.1325 10.0000
10.0000 10.5033 11.1325 11.1325 10.5033 10.0000
10.0000 10.0000 10.0000 10.0000 10.0000 10.0000
--------------------------------------------------------------------------------
the species c( 4) values are:
10.0000 10.0000 10.0000 10.0000 10.0000 10.0000
10.0000 10.6711 11.5099 11.5099 10.6711 10.0000
10.0000 11.5099 13.3974 13.3974 11.5099 10.0000
10.0000 11.5099 13.3974 13.3974 11.5099 10.0000
10.0000 10.6711 11.5099 11.5099 10.6711 10.0000
10.0000 10.0000 10.0000 10.0000 10.0000 10.0000
--------------------------------------------------------------------------------
the species c( 5) values are:
10.0000 10.0000 10.0000 10.0000 10.0000 10.0000
10.0000 10.8389 11.8874 11.8874 10.8389 10.0000
10.0000 11.8874 14.2467 14.2467 11.8874 10.0000
10.0000 11.8874 14.2467 14.2467 11.8874 10.0000
10.0000 10.8389 11.8874 11.8874 10.8389 10.0000
10.0000 10.0000 10.0000 10.0000 10.0000 10.0000
--------------------------------------------------------------------------------
the species c( 6) values are:
10.0000 10.0000 10.0000 10.0000 10.0000 10.0000
10.0000 11.0066 12.2649 12.2649 11.0066 10.0000
10.0000 12.2649 15.0961 15.0961 12.2649 10.0000
10.0000 12.2649 15.0961 15.0961 12.2649 10.0000
10.0000 11.0066 12.2649 12.2649 11.0066 10.0000
10.0000 10.0000 10.0000 10.0000 10.0000 10.0000
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
At time t = 0.10000000E-05
--------------------------------------------------------------------------------
the species c( 1) values are:
9.99991 9.99992 9.99993 9.99993 9.99993 9.99992
9.99992 10.1677 10.3774 10.3774 10.1677 9.99993
9.99993 10.3774 10.8492 10.8492 10.3774 9.99993
9.99993 10.3774 10.8492 10.8492 10.3774 9.99993
9.99992 10.1677 10.3774 10.3774 10.1677 9.99992
9.99991 9.99992 9.99993 9.99993 9.99992 9.99991
--------------------------------------------------------------------------------
the species c( 2) values are:
9.99991 9.99993 9.99995 9.99995 9.99993 9.99992
9.99993 10.3355 10.7549 10.7549 10.3355 9.99993
9.99995 10.7549 11.6985 11.6985 10.7549 9.99995
9.99995 10.7549 11.6985 11.6985 10.7549 9.99995
9.99993 10.3355 10.7549 10.7549 10.3355 9.99993
9.99991 9.99993 9.99995 9.99995 9.99993 9.99991
--------------------------------------------------------------------------------
the species c( 3) values are:
9.99991 9.99994 9.99997 9.99997 9.99994 9.99992
9.99994 10.5032 11.1323 11.1323 10.5032 9.99994
9.99997 11.1323 12.5478 12.5478 11.1323 9.99997
9.99997 11.1323 12.5478 12.5478 11.1323 9.99997
9.99994 10.5032 11.1323 11.1323 10.5032 9.99994
9.99991 9.99994 9.99997 9.99997 9.99994 9.99991
--------------------------------------------------------------------------------
the species c( 4) values are:
13.4987 13.4987 13.4987 13.4987 13.4987 13.4987
13.4987 14.5503 15.8929 15.8929 14.5503 13.4987
13.4987 15.8929 19.0303 19.0303 15.8929 13.4987
13.4987 15.8929 19.0303 19.0303 15.8929 13.4987
13.4987 14.5503 15.8929 15.8929 14.5503 13.4987
13.4987 13.4987 13.4987 13.4987 13.4987 13.4987
--------------------------------------------------------------------------------
the species c( 5) values are:
13.4987 13.4987 13.4987 13.4987 13.4987 13.4987
13.4987 14.7791 16.4141 16.4141 14.7791 13.4987
13.4987 16.4141 20.2367 20.2367 16.4141 13.4987
13.4987 16.4141 20.2367 20.2367 16.4141 13.4987
13.4987 14.7791 16.4141 16.4141 14.7791 13.4987
13.4987 13.4987 13.4987 13.4987 13.4987 13.4987
--------------------------------------------------------------------------------
the species c( 6) values are:
13.4987 13.4987 13.4988 13.4987 13.4987 13.4987
13.4987 15.0078 16.9353 16.9353 15.0078 13.4987
13.4988 16.9353 21.4431 21.4431 16.9353 13.4987
13.4988 16.9353 21.4431 21.4431 16.9353 13.4988
13.4987 15.0078 16.9353 16.9353 15.0078 13.4987
13.4987 13.4987 13.4988 13.4988 13.4987 13.4987
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
At time t = 0.10000000E-02
--------------------------------------------------------------------------------
the species c( 1) values are:
9.90702 9.91664 9.92836 9.93033 9.92253 9.91674
9.91472 10.0746 10.2769 10.2785 10.0795 9.92253
9.92446 10.2748 10.7181 10.7194 10.2785 9.93033
9.92445 10.2744 10.7173 10.7181 10.2769 9.92836
9.91469 10.0734 10.2744 10.2748 10.0746 9.91664
9.90697 9.91469 9.92445 9.92446 9.91472 9.90702
--------------------------------------------------------------------------------
the species c( 2) values are:
9.90741 9.92474 9.94623 9.94820 9.93064 9.91713
9.92282 10.2412 10.6440 10.6457 10.2461 9.93064
9.94232 10.6419 11.5267 11.5281 10.6457 9.94820
9.94231 10.6415 11.5258 11.5267 10.6440 9.94623
9.92279 10.2400 10.6415 10.6419 10.2412 9.92474
9.90736 9.92279 9.94231 9.94232 9.92282 9.90741
--------------------------------------------------------------------------------
the species c( 3) values are:
9.90780 9.93284 9.96409 9.96606 9.93874 9.91752
9.93092 10.4078 11.0109 11.0127 10.4127 9.93874
9.96018 11.0088 12.3339 12.3354 11.0127 9.96606
9.96017 11.0083 12.3329 12.3339 11.0109 9.96409
9.93089 10.4065 11.0083 11.0088 10.4078 9.93284
9.90776 9.93089 9.96017 9.96018 9.93092 9.90780
--------------------------------------------------------------------------------
the species c( 4) values are:
297231. 297749. 298393. 298451. 297925. 297520.
297692. 307244. 319327. 319378. 307390. 297925.
298276. 319264. 345799. 345840. 319378. 298451.
298276. 319252. 345771. 345799. 319327. 298393.
297691. 307208. 319252. 319264. 307244. 297749.
297229. 297691. 298276. 298276. 297692. 297231.
--------------------------------------------------------------------------------
the species c( 5) values are:
297231. 297749. 298393. 298451. 297925. 297520.
297692. 307244. 319327. 319378. 307390. 297925.
298276. 319264. 345799. 345840. 319378. 298451.
298276. 319252. 345771. 345799. 319327. 298393.
297691. 307208. 319252. 319264. 307244. 297749.
297229. 297691. 298276. 298276. 297692. 297231.
--------------------------------------------------------------------------------
the species c( 6) values are:
297231. 297749. 298393. 298451. 297925. 297520.
297692. 307244. 319327. 319378. 307390. 297925.
298276. 319264. 345799. 345840. 319378. 298451.
298276. 319252. 345771. 345799. 319327. 298393.
297691. 307208. 319252. 319264. 307244. 297749.
297229. 297691. 298276. 298276. 297692. 297231.
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
At time t = 0.10000000E+01
--------------------------------------------------------------------------------
the species c( 1) values are:
1.58846 1.59918 1.62146 1.64759 1.67030 1.68143
1.58527 1.59498 1.61542 1.63946 1.66027 1.67030
1.57751 1.58542 1.60234 1.62229 1.63946 1.64759
1.56815 1.57406 1.58700 1.60234 1.61542 1.62146
1.56043 1.56457 1.57406 1.58542 1.59498 1.59918
1.55727 1.56043 1.56815 1.57751 1.58527 1.58846
--------------------------------------------------------------------------------
the species c( 2) values are:
1.59061 1.60135 1.62365 1.64981 1.67255 1.68369
1.58742 1.59714 1.61761 1.64167 1.66251 1.67255
1.57965 1.58757 1.60451 1.62449 1.64167 1.64981
1.57028 1.57620 1.58916 1.60451 1.61761 1.62365
1.56255 1.56670 1.57620 1.58757 1.59714 1.60135
1.55939 1.56255 1.57028 1.57965 1.58742 1.59061
--------------------------------------------------------------------------------
the species c( 3) values are:
1.59265 1.60340 1.62572 1.65191 1.67468 1.68583
1.58946 1.59918 1.61967 1.64377 1.66462 1.67468
1.58168 1.58960 1.60656 1.62656 1.64377 1.65191
1.57230 1.57823 1.59119 1.60656 1.61967 1.62572
1.56456 1.56872 1.57823 1.58960 1.59918 1.60340
1.56140 1.56456 1.57230 1.58168 1.58946 1.59265
--------------------------------------------------------------------------------
the species c( 4) values are:
47716.6 48038.6 48707.3 49491.7 50173.7 50507.6
47621.0 47912.3 48526.1 49247.9 49872.6 50173.7
47388.0 47625.3 48133.2 48732.4 49247.9 49491.7
47106.8 47284.3 47672.8 48133.2 48526.1 48707.3
46874.9 46999.4 47284.3 47625.3 47912.3 48038.6
46780.1 46874.9 47106.8 47388.0 47621.0 47716.6
--------------------------------------------------------------------------------
the species c( 5) values are:
47716.6 48038.6 48707.3 49491.7 50173.7 50507.6
47621.0 47912.3 48526.1 49247.9 49872.6 50173.7
47388.0 47625.3 48133.2 48732.4 49247.9 49491.7
47106.8 47284.3 47672.8 48133.2 48526.1 48707.3
46874.9 46999.4 47284.3 47625.3 47912.3 48038.6
46780.1 46874.9 47106.8 47388.0 47621.0 47716.6
--------------------------------------------------------------------------------
the species c( 6) values are:
47716.6 48038.6 48707.3 49491.7 50173.7 50507.6
47621.0 47912.3 48526.1 49247.9 49872.6 50173.7
47388.0 47625.3 48133.2 48732.4 49247.9 49491.7
47106.8 47284.3 47672.8 48133.2 48526.1 48707.3
46874.9 46999.4 47284.3 47625.3 47912.3 48038.6
46780.1 46874.9 47106.8 47388.0 47621.0 47716.6
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
At time t = 0.40000000E+01
--------------------------------------------------------------------------------
the species c( 1) values are:
1.19534 1.20367 1.22108 1.24156 1.25934 1.26799
1.19279 1.20034 1.21635 1.23521 1.25152 1.25934
1.18656 1.19272 1.20601 1.22172 1.23521 1.24156
1.17903 1.18367 1.19388 1.20601 1.21635 1.22108
1.17283 1.17611 1.18367 1.19272 1.20034 1.20367
1.17031 1.17283 1.17903 1.18656 1.19279 1.19534
--------------------------------------------------------------------------------
the species c( 2) values are:
1.19537 1.20370 1.22112 1.24159 1.25937 1.26802
1.19282 1.20037 1.21638 1.23525 1.25156 1.25937
1.18659 1.19276 1.20605 1.22175 1.23525 1.24159
1.17906 1.18370 1.19391 1.20605 1.21638 1.22112
1.17287 1.17615 1.18370 1.19276 1.20037 1.20370
1.17034 1.17287 1.17906 1.18659 1.19282 1.19537
--------------------------------------------------------------------------------
the species c( 3) values are:
1.19540 1.20373 1.22115 1.24163 1.25940 1.26806
1.19286 1.20040 1.21641 1.23528 1.25159 1.25940
1.18662 1.19279 1.20608 1.22179 1.23528 1.24163
1.17910 1.18373 1.19395 1.20608 1.21641 1.22115
1.17290 1.17618 1.18373 1.19279 1.20040 1.20373
1.17037 1.17290 1.17910 1.18662 1.19286 1.19540
--------------------------------------------------------------------------------
the species c( 4) values are:
35860.3 36109.8 36632.0 37246.1 37779.1 38038.3
35783.8 36010.0 36490.0 37055.9 37544.9 37779.1
35596.8 35781.6 36180.1 36651.2 37055.9 37246.1
35371.0 35510.0 35816.3 36180.1 36490.0 36632.0
35185.1 35283.4 35510.0 35781.6 36010.0 36109.8
35109.4 35185.1 35371.0 35596.8 35783.8 35860.3
--------------------------------------------------------------------------------
the species c( 5) values are:
35860.3 36109.8 36632.0 37246.1 37779.1 38038.3
35783.8 36010.0 36490.0 37055.9 37544.9 37779.1
35596.8 35781.6 36180.1 36651.2 37055.9 37246.1
35371.0 35510.0 35816.3 36180.1 36490.0 36632.0
35185.1 35283.4 35510.0 35781.6 36010.0 36109.8
35109.4 35185.1 35371.0 35596.8 35783.8 35860.3
--------------------------------------------------------------------------------
the species c( 6) values are:
35860.3 36109.8 36632.0 37246.1 37779.1 38038.3
35783.8 36010.0 36490.0 37055.9 37544.9 37779.1
35596.8 35781.6 36180.1 36651.2 37055.9 37246.1
35371.0 35510.0 35816.3 36180.1 36490.0 36632.0
35185.1 35283.4 35510.0 35781.6 36010.0 36109.8
35109.4 35185.1 35371.0 35596.8 35783.8 35860.3
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
At time t = 0.70000000E+01
--------------------------------------------------------------------------------
the species c( 1) values are:
1.18854 1.19682 1.21415 1.23453 1.25221 1.26082
1.18600 1.19351 1.20944 1.22821 1.24444 1.25221
1.17980 1.18593 1.19916 1.21479 1.22821 1.23453
1.17231 1.17692 1.18708 1.19916 1.20944 1.21415
1.16614 1.16940 1.17692 1.18593 1.19351 1.19682
1.16363 1.16614 1.17231 1.17980 1.18600 1.18854
--------------------------------------------------------------------------------
the species c( 2) values are:
1.18854 1.19682 1.21415 1.23453 1.25221 1.26082
1.18600 1.19351 1.20944 1.22821 1.24444 1.25221
1.17980 1.18593 1.19916 1.21479 1.22821 1.23453
1.17231 1.17692 1.18708 1.19916 1.20944 1.21415
1.16614 1.16940 1.17692 1.18593 1.19351 1.19682
1.16363 1.16614 1.17231 1.17980 1.18600 1.18854
--------------------------------------------------------------------------------
the species c( 3) values are:
1.18854 1.19682 1.21415 1.23453 1.25221 1.26082
1.18600 1.19351 1.20944 1.22821 1.24444 1.25221
1.17980 1.18593 1.19916 1.21479 1.22821 1.23453
1.17231 1.17692 1.18709 1.19916 1.20944 1.21415
1.16614 1.16940 1.17692 1.18593 1.19351 1.19682
1.16363 1.16614 1.17231 1.17980 1.18600 1.18854
--------------------------------------------------------------------------------
the species c( 4) values are:
35655.3 35903.5 36423.1 37034.0 37564.3 37822.2
35579.2 35804.2 36281.9 36844.8 37331.4 37564.3
35393.1 35576.9 35973.5 36442.2 36844.8 37034.0
35168.3 35306.6 35611.4 35973.5 36281.9 36423.1
34983.2 35081.1 35306.6 35576.9 35804.2 35903.5
34907.9 34983.2 35168.3 35393.1 35579.2 35655.3
--------------------------------------------------------------------------------
the species c( 5) values are:
35655.3 35903.5 36423.1 37034.0 37564.3 37822.2
35579.2 35804.2 36281.9 36844.8 37331.4 37564.3
35393.1 35576.9 35973.5 36442.2 36844.8 37034.0
35168.3 35306.6 35611.4 35973.5 36281.9 36423.1
34983.2 35081.1 35306.6 35576.9 35804.2 35903.5
34907.9 34983.2 35168.3 35393.1 35579.2 35655.3
--------------------------------------------------------------------------------
the species c( 6) values are:
35655.3 35903.5 36423.1 37034.0 37564.3 37822.2
35579.2 35804.2 36281.9 36844.8 37331.4 37564.3
35393.1 35576.9 35973.5 36442.2 36844.8 37034.0
35168.3 35306.6 35611.4 35973.5 36281.9 36423.1
34983.2 35081.1 35306.6 35576.9 35804.2 35903.5
34907.9 34983.2 35168.3 35393.1 35579.2 35655.3
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
At time t = 0.10000000E+02
--------------------------------------------------------------------------------
the species c( 1) values are:
1.18838 1.19666 1.21399 1.23436 1.25205 1.26065
1.18584 1.19335 1.20928 1.22805 1.24428 1.25205
1.17964 1.18577 1.19899 1.21463 1.22805 1.23436
1.17215 1.17676 1.18692 1.19899 1.20928 1.21399
1.16598 1.16924 1.17676 1.18577 1.19335 1.19666
1.16347 1.16598 1.17215 1.17964 1.18584 1.18838
--------------------------------------------------------------------------------
the species c( 2) values are:
1.18838 1.19666 1.21399 1.23436 1.25205 1.26065
1.18584 1.19335 1.20928 1.22805 1.24428 1.25205
1.17964 1.18577 1.19899 1.21462 1.22805 1.23436
1.17215 1.17676 1.18692 1.19899 1.20928 1.21399
1.16598 1.16924 1.17676 1.18577 1.19335 1.19666
1.16347 1.16598 1.17215 1.17964 1.18584 1.18838
--------------------------------------------------------------------------------
the species c( 3) values are:
1.18838 1.19666 1.21399 1.23436 1.25205 1.26065
1.18584 1.19335 1.20928 1.22805 1.24428 1.25205
1.17964 1.18577 1.19899 1.21462 1.22805 1.23436
1.17215 1.17676 1.18692 1.19899 1.20928 1.21399
1.16598 1.16924 1.17676 1.18577 1.19335 1.19666
1.16347 1.16598 1.17215 1.17964 1.18584 1.18838
--------------------------------------------------------------------------------
the species c( 4) values are:
35650.5 35898.7 36418.2 37029.1 37559.4 37817.2
35574.4 35799.4 36277.0 36839.9 37326.5 37559.4
35388.3 35572.1 35968.6 36437.3 36839.9 37029.1
35163.6 35301.8 35606.6 35968.6 36277.0 36418.2
34978.5 35076.4 35301.8 35572.1 35799.4 35898.7
34903.1 34978.5 35163.6 35388.3 35574.4 35650.5
--------------------------------------------------------------------------------
the species c( 5) values are:
35650.5 35898.7 36418.2 37029.1 37559.4 37817.2
35574.4 35799.4 36277.0 36839.9 37326.5 37559.4
35388.3 35572.1 35968.6 36437.3 36839.9 37029.1
35163.6 35301.8 35606.6 35968.6 36277.0 36418.2
34978.5 35076.4 35301.8 35572.1 35799.4 35898.7
34903.1 34978.5 35163.6 35388.3 35574.4 35650.5
--------------------------------------------------------------------------------
the species c( 6) values are:
35650.5 35898.7 36418.2 37029.1 37559.4 37817.2
35574.4 35799.4 36277.0 36839.9 37326.5 37559.4
35388.3 35572.1 35968.6 36437.3 36839.9 37029.1
35163.6 35301.8 35606.6 35968.6 36277.0 36418.2
34978.5 35076.4 35301.8 35572.1 35799.4 35898.7
34903.1 34978.5 35163.6 35388.3 35574.4 35650.5
--------------------------------------------------------------------------------
==========Source and Output for LSODKR Demonstration Program====================
c-----------------------------------------------------------------------
c Demonstration program for the SLSODKR package.
c This is the version of 27 April 2005.
c
c This version is in single precision.
c
c An ODE system is generated from the following 2-species diurnal
c kinetics advection-diffusion PDE system in 2 space dimensions:
c
c dc(i)/dt = Kh*(d/dx)**2 c(i) + V*dc(i)/dx + (d/dz)(Kv(z)*dc(i)/dz)
c + Ri(c1,c2,t) for i = 1,2, where
c R1(c1,c2,t) = -q1*c1*c3 - q2*c1*c2 + 2*q3(t)*c3 + q4(t)*c2 ,
c R2(c1,c2,t) = q1*c1*c3 - q2*c1*c2 - q4(t)*c2 ,
c Kv(z) = Kv0*exp(z/5) ,
c Kh, V, Kv0, q1, q2, and c3 are constants, and q3(t) and q4(t)
c vary diurnally. The species are oxygen singlet and ozone.
c The problem is posed on the square
c 0 .le. x .le. 20, 30 .le. z .le. 50 (all in km),
c with homogeneous Neumann boundary conditions, and for time t in
c 0 .le. t .le. 86400 sec (1 day).
c
c The PDE system is treated by central differences on a uniform
c 10 x 10 mesh, with simple polynomial initial profiles.
c
c The problem is solved with SLSODKR, with the BDF/GMRES method and
c the block-diagonal part of the Jacobian as a left preconditioner.
c At intervals of 7200 sec (2 hrs), output includes sample values
c of c1, c2, and c2tot = total of all c2 values.
c
c Roots of the function g = d(c2tot)/dt are found, i.e. the points at
c which the total c2 (ozone) is stationary.
c
c Note: The preconditioner routines call LINPACK routines SGEFA, SGESL,
c and the BLAS routines SCOPY and SSCAL.
c-----------------------------------------------------------------------
external fdem, jacbd, solbd, gdem
integer mx, mz, mm, iout, istate, iwork, jacflg, jpre, jroot,
1 jx, jz, leniw, lenrw, liw, lrw, mf, neq, nst, nsfi, nfe,
2 nge, npe, njev, nps, nni, nli, ncfn, ncfl
real q1,q2,q3,q4, a3,a4, om, c3, dz, hdco, vdco, haco,
1 dkh, vel, dkv0, halfda, pi, twohr, rtol, floor,
2 dx, atol, t, tout, x, cx, z, cz, y, rwork, c2tot, avdim
common /pcom/ q1,q2,q3,q4,a3,a4,om,c3,dz,hdco,vdco,haco,mx,mz,mm
dimension y(2,10,10), rwork(4264), iwork(235)
data dkh/4.0e-6/, vel/0.001e0/, dkv0/1.0e-8/, halfda/4.32e4/,
1 pi/3.1415926535898e0/, twohr/7200.0e0/, rtol/1.0e-5/,
2 floor/100.0e0/, lrw/4264/, liw/235/, mf/22/, jpre/1/, jacflg/1/
c
c Load Common block of problem parameters.
mx = 10
mz = 10
mm = mx*mz
q1 = 1.63e-16
q2 = 4.66e-16
a3 = 22.62e0
a4 = 7.601e0
om = pi/halfda
c3 = 3.7e16
dx = 20.0e0/(mx - 1.0e0)
dz = 20.0e0/(mz - 1.0e0)
hdco = dkh/dx**2
haco = vel/(2.0e0*dx)
vdco = (1.0e0/dz**2)*dkv0
c Set other input arguments.
atol = rtol*floor
neq = 2*mx*mz
iwork(1) = 8*mx*mz
iwork(2) = neq
iwork(3) = jpre
iwork(4) = jacflg
t = 0.0e0
tout = 0.0e0
jroot = 0
istate = 1
c Initialize values for tout = 0 output.
iwork(11) = 0
iwork(14) = 0
rwork(11) = 0.0e0
c Set initial profiles.
do 20 jz = 1,mz
z = 30.0e0 + (jz - 1.0e0)*dz
cz = (0.1e0*(z - 40.0e0))**2
cz = 1.0e0 - cz + 0.5e0*cz**2
do 10 jx = 1,mx
x = (jx - 1.0e0)*dx
cx = (0.1e0*(x - 10.0e0))**2
cx = 1.0e0 - cx + 0.5e0*cx**2
y(1,jx,jz) = 1.0e6*cx*cz
y(2,jx,jz) = 1.0e12*cx*cz
10 continue
20 continue
c
c Write heading, problem parameters, solution parameters.
write(6,30) mx, mz, mf, rtol, atol
30 format('Demonstration program for SLSODKR package'//
1 '2D diurnal kinetics-transport PDE system with 2 species'/
2 'Spatial mesh is',i3,' by',i3/'Method flag is mf =',i3,
3 ' Tolerances are rtol =',e8.1,' atol =',e8.1/
4 'Left preconditioner uses block-diagonal part of Jacobian'/
5 'Root function finds stationary points of total ozone,'/
6 ' i.e. roots of (d/dt)(sum of c2 over all mesh points)'/)
c
c Loop over output points, call SLSODKR, print sample solution values.
do 70 iout = 1,13
40 call slsodkr (fdem, neq, y, t, tout, 1, rtol, atol, 1, istate,
1 0, rwork, lrw, iwork, liw, jacbd, solbd, mf, gdem, 1, jroot)
write(6,50) t,iwork(11),iwork(14),rwork(11)
50 format(/' t =',e10.3,4x,'no. steps =',i5,
1 ' order =',i2,' stepsize =',e10.3)
call c2sum (y, mx, mz, c2tot)
write(6,60) y(1,1,1), y(1,5,5), y(1,10,10),
1 y(2,1,1), y(2,5,5), y(2,10,10)
60 format(' c1 (bot.left/middle/top rt.) =',3e12.3/
1 ' c2 (bot.left/middle/top rt.) =',3e12.3)
write(6,62)c2tot,jroot
62 format(' total c2 =',e15.6,
1 ' jroot =',i2,' (1 = root found, 0 = no root)')
if (istate .lt. 0) then
write(6,65)istate
65 format('SLSODKR returned istate = ',i3)
go to 75
endif
if (istate .eq. 3) then
istate = 2
go to 40
endif
tout = tout + twohr
70 continue
c
c Print final statistics.
75 lenrw = iwork(17)
leniw = iwork(18)
nst = iwork(11)
nsfi = iwork(24)
nfe = iwork(12)
nge = iwork(10)
npe = iwork(13)
njev = iwork(25)
nps = iwork(21)
nni = iwork(19)
nli = iwork(20)
avdim = real(nli)/real(nni)
ncfn = iwork(22)
ncfl = iwork(23)
write (6,80) lenrw,leniw,nst,nsfi,nfe,nge,npe,njev,nps,nni,nli,
1 avdim,ncfn,ncfl
80 format(//' Final statistics:'/
1 ' rwork size =',i5,5x,' iwork size =',i4/
2 ' number of steps =',i5,5x,'no. fnal. iter. steps =',i5/
3 ' number of f evals. =',i5,5x,'number of g evals. =',i5/
4 ' number of prec. evals. =',i5,5x,'number of Jac. evals. =',i5/
5 ' number of prec. solves =',i5/
6 ' number of nonl. iters. =',i5,5x,'number of lin. iters. =',i5/
7 ' average Krylov subspace dimension (nli/nni) =',f8.4/
8 ' number of conv. failures: nonlinear =',i3,' linear =',i3)
stop
end
subroutine fdem (neq, t, y, ydot)
integer neq, mx, mz, mm,
1 iblok, iblok0, idn, iup, ileft, iright, jx, jz
real t, y(2,*), ydot(2,*),
1 q1, q2, q3, q4, a3, a4, om, c3, dz, hdco, vdco, haco,
2 c1, c1dn, c1up, c1lt, c1rt, c2, c2dn, c2up, c2lt, c2rt,
3 czdn, czup, horad1, hord1, horad2, hord2, qq1, qq2, qq3, qq4,
4 rkin1, rkin2, s, vertd1, vertd2, zdn, zup
common /pcom/ q1,q2,q3,q4,a3,a4,om,c3,dz,hdco,vdco,haco,mx,mz,mm
c
c Set diurnal rate coefficients.
s = sin(om*t)
if (s .gt. 0.0e0) then
q3 = exp(-a3/s)
q4 = exp(-a4/s)
else
q3 = 0.0e0
q4 = 0.0e0
endif
c Loop over all grid points.
do 20 jz = 1,mz
zdn = 30.0e0 + (jz - 1.5e0)*dz
zup = zdn + dz
czdn = vdco*exp(0.2e0*zdn)
czup = vdco*exp(0.2e0*zup)
iblok0 = (jz-1)*mx
idn = -mx
if (jz .eq. 1) idn = mx
iup = mx
if (jz .eq. mz) iup = -mx
do 10 jx = 1,mx
iblok = iblok0 + jx
c1 = y(1,iblok)
c2 = y(2,iblok)
c Set kinetic rate terms.
qq1 = q1*c1*c3
qq2 = q2*c1*c2
qq3 = q3*c3
qq4 = q4*c2
rkin1 = -qq1 - qq2 + 2.0e0*qq3 + qq4
rkin2 = qq1 - qq2 - qq4
c Set vertical diffusion terms.
c1dn = y(1,iblok+idn)
c2dn = y(2,iblok+idn)
c1up = y(1,iblok+iup)
c2up = y(2,iblok+iup)
vertd1 = czup*(c1up - c1) - czdn*(c1 - c1dn)
vertd2 = czup*(c2up - c2) - czdn*(c2 - c2dn)
c Set horizontal diffusion and advection terms.
ileft = -1
if (jx .eq. 1) ileft = 1
iright = 1
if (jx .eq. mx) iright = -1
c1lt = y(1,iblok+ileft)
c2lt = y(2,iblok+ileft)
c1rt = y(1,iblok+iright)
c2rt = y(2,iblok+iright)
hord1 = hdco*(c1rt - 2.0e0*c1 + c1lt)
hord2 = hdco*(c2rt - 2.0e0*c2 + c2lt)
horad1 = haco*(c1rt - c1lt)
horad2 = haco*(c2rt - c2lt)
c Load all terms into ydot.
ydot(1,iblok) = vertd1 + hord1 + horad1 + rkin1
ydot(2,iblok) = vertd2 + hord2 + horad2 + rkin2
10 continue
20 continue
return
end
subroutine gdem (neq, t, y, ng, gout)
integer neq, ng, mx, mz, mm,
1 iblok, iblok0, idn, iup, ileft, iright, jx, jz
real t, y(2,*), gout,
1 q1, q2, q3, q4, a3, a4, om, c3, dz, hdco, vdco, haco,
2 c1, c2, c2dn, c2up, c2lt, c2rt, c2dot, czdn, czup, horad2,
3 hord2, qq1, qq2, qq4, rkin2, s, sum, vertd2, zdn, zup
common /pcom/ q1,q2,q3,q4,a3,a4,om,c3,dz,hdco,vdco,haco,mx,mz,mm
c
c This routine computes the rates for c2 and adds them.
c
c Set diurnal rate coefficient q4.
s = sin(om*t)
if (s .gt. 0.0e0) then
q4 = exp(-a4/s)
else
q4 = 0.0e0
endif
sum = 0.0e0
c Loop over all grid points.
do 20 jz = 1,mz
zdn = 30.0e0 + (jz - 1.5e0)*dz
zup = zdn + dz
czdn = vdco*exp(0.2e0*zdn)
czup = vdco*exp(0.2e0*zup)
iblok0 = (jz-1)*mx
idn = -mx
if (jz .eq. 1) idn = mx
iup = mx
if (jz .eq. mz) iup = -mx
do 10 jx = 1,mx
iblok = iblok0 + jx
c1 = y(1,iblok)
c2 = y(2,iblok)
c Set kinetic rate term for c2.
qq1 = q1*c1*c3
qq2 = q2*c1*c2
qq4 = q4*c2
rkin2 = qq1 - qq2 - qq4
c Set vertical diffusion terms for c2.
c2dn = y(2,iblok+idn)
c2up = y(2,iblok+iup)
vertd2 = czup*(c2up - c2) - czdn*(c2 - c2dn)
c Set horizontal diffusion and advection terms for c2.
ileft = -1
if (jx .eq. 1) ileft = 1
iright = 1
if (jx .eq. mx) iright = -1
c2lt = y(2,iblok+ileft)
c2rt = y(2,iblok+iright)
hord2 = hdco*(c2rt - 2.0e0*c2 + c2lt)
horad2 = haco*(c2rt - c2lt)
c Load all terms into c2dot and sum.
c2dot = vertd2 + hord2 + horad2 + rkin2
sum = sum + c2dot
10 continue
20 continue
gout = sum
return
end
subroutine jacbd (f, neq, t, y, ysv, rewt, f0, f1, hl0, jok,
1 bd, ipbd, ier)
external f
integer neq, jok, ipbd(2,*), ier, mx, mz, mm,
1 iblok, iblok0, jx, jz, lenbd
real t, y(2,*), ysv(neq), rewt(neq), f0(neq), f1(neq),
1 hl0, bd(2,2,*),
2 q1, q2, q3, q4, a3, a4, om, c3, dz, hdco, vdco, haco,
3 c1, c2, czdn, czup, diag, temp, zdn, zup
common /pcom/ q1,q2,q3,q4,a3,a4,om,c3,dz,hdco,vdco,haco,mx,mz,mm
c
lenbd = 4*mm
c If jok = 1, copy saved block-diagonal approximate Jacobian into bd.
if (jok .eq. 1) then
call scopy (lenbd, bd(1,1,mm+1), 1, bd, 1)
go to 30
endif
c
c If jok = -1, compute and save diagonal Jacobian blocks
c (using q3 and q4 values computed on last f call).
do 20 jz = 1,mz
zdn = 30.0e0 + (jz - 1.5e0)*dz
zup = zdn + dz
czdn = vdco*exp(0.2e0*zdn)
czup = vdco*exp(0.2e0*zup)
diag = -(czdn + czup + 2.0e0*hdco)
iblok0 = (jz-1)*mx
do 10 jx = 1,mx
iblok = iblok0 + jx
c1 = y(1,iblok)
c2 = y(2,iblok)
bd(1,1,iblok) = (-q1*c3 - q2*c2) + diag
bd(1,2,iblok) = -q2*c1 + q4
bd(2,1,iblok) = q1*c3 - q2*c2
bd(2,2,iblok) = (-q2*c1 - q4) + diag
10 continue
20 continue
call scopy (lenbd, bd, 1, bd(1,1,mm+1), 1)
c Scale by -hl0, add identity matrix and LU-decompose blocks.
30 temp = -hl0
call sscal (lenbd, temp, bd, 1)
do 40 iblok = 1,mm
bd(1,1,iblok) = bd(1,1,iblok) + 1.0e0
bd(2,2,iblok) = bd(2,2,iblok) + 1.0e0
call sgefa (bd(1,1,iblok), 2, 2, ipbd(1,iblok), ier)
if (ier .ne. 0) return
40 continue
return
end
subroutine solbd (neq, t, y, f0, wk, hl0, bd, ipbd, v, lr, ier)
integer neq, ipbd(2,*), lr, ier, mx, mz, mm, i
real t, y(neq), f0(neq), wk(neq), hl0, bd(2,2,*), v(2,*),
2 q1, q2, q3, q4, a3, a4, om, c3, dz, hdco, vdco, haco
common /pcom/ q1,q2,q3,q4,a3,a4,om,c3,dz,hdco,vdco,haco,mx,mz,mm
c Solve the block-diagonal system Px = v using LU factors stored in bd
c and pivot data in ipbd, and return the solution in v.
ier = 0
do 10 i = 1,mm
call sgesl (bd(1,1,i), 2, 2, ipbd(1,i), v(1,i), 0)
10 continue
return
end
subroutine c2sum (y, mx, mz, c2tot)
integer mx, mz, jx, jz
real y(2,mx,mz), c2tot, sum
c Sum the c2 values.
sum = 0.0e0
do 20 jz = 1,mz
do 20 jx = 1,mx
20 sum = sum + y(2,jx,jz)
c2tot = sum
return
end
................................................................................
Demonstration program for DLSODKR package
2D diurnal kinetics-transport PDE system with 2 species
Spatial mesh is 10 by 10
Method flag is mf = 22 Tolerances are rtol = 0.1E-04 atol = 0.1E-02
Left preconditioner uses block-diagonal part of Jacobian
Root function finds stationary points of total ozone,
i.e. roots of (d/dt)(sum of c2 over all mesh points)
t = 0.000E+00 no. steps = 0 order = 0 stepsize = 0.000E+00
c1 (bot.left/middle/top rt.) = 0.250E+06 0.976E+06 0.250E+06
c2 (bot.left/middle/top rt.) = 0.250E+12 0.976E+12 0.250E+12
total c2 = 0.547546E+14 jroot = 0 (1 = root found, 0 = no root)
t = 0.184E+03 no. steps = 132 order = 2 stepsize = 0.138E+03
c1 (bot.left/middle/top rt.) = 0.438E-07 0.171E-06 0.440E-07
c2 (bot.left/middle/top rt.) = 0.250E+12 0.979E+12 0.251E+12
total c2 = 0.547575E+14 jroot = 1 (1 = root found, 0 = no root)
t = 0.720E+04 no. steps = 192 order = 5 stepsize = 0.158E+03
c1 (bot.left/middle/top rt.) = 0.105E+05 0.296E+05 0.112E+05
c2 (bot.left/middle/top rt.) = 0.253E+12 0.715E+12 0.270E+12
total c2 = 0.503689E+14 jroot = 0 (1 = root found, 0 = no root)
t = 0.144E+05 no. steps = 222 order = 5 stepsize = 0.352E+03
c1 (bot.left/middle/top rt.) = 0.666E+07 0.532E+07 0.730E+07
c2 (bot.left/middle/top rt.) = 0.258E+12 0.206E+12 0.283E+12
total c2 = 0.405024E+14 jroot = 0 (1 = root found, 0 = no root)
t = 0.183E+05 no. steps = 255 order = 5 stepsize = 0.270E+03
c1 (bot.left/middle/top rt.) = 0.187E+08 0.551E+07 0.206E+08
c2 (bot.left/middle/top rt.) = 0.269E+12 0.694E+11 0.297E+12
total c2 = 0.379640E+14 jroot = 1 (1 = root found, 0 = no root)
t = 0.216E+05 no. steps = 265 order = 5 stepsize = 0.409E+03
c1 (bot.left/middle/top rt.) = 0.266E+08 0.104E+08 0.293E+08
c2 (bot.left/middle/top rt.) = 0.299E+12 0.103E+12 0.331E+12
total c2 = 0.397443E+14 jroot = 0 (1 = root found, 0 = no root)
t = 0.252E+05 no. steps = 274 order = 5 stepsize = 0.409E+03
c1 (bot.left/middle/top rt.) = 0.218E+08 0.189E+08 0.241E+08
c2 (bot.left/middle/top rt.) = 0.331E+12 0.284E+12 0.366E+12
total c2 = 0.417179E+14 jroot = 1 (1 = root found, 0 = no root)
t = 0.288E+05 no. steps = 295 order = 5 stepsize = 0.142E+03
c1 (bot.left/middle/top rt.) = 0.870E+07 0.129E+08 0.965E+07
c2 (bot.left/middle/top rt.) = 0.338E+12 0.503E+12 0.375E+12
total c2 = 0.395883E+14 jroot = 0 (1 = root found, 0 = no root)
t = 0.360E+05 no. steps = 325 order = 5 stepsize = 0.119E+03
c1 (bot.left/middle/top rt.) = 0.140E+05 0.203E+05 0.156E+05
c2 (bot.left/middle/top rt.) = 0.339E+12 0.489E+12 0.377E+12
total c2 = 0.303138E+14 jroot = 0 (1 = root found, 0 = no root)
t = 0.405E+05 no. steps = 371 order = 5 stepsize = 0.123E+03
c1 (bot.left/middle/top rt.) = 0.116E-05 0.750E-06 0.130E-05
c2 (bot.left/middle/top rt.) = 0.339E+12 0.218E+12 0.378E+12
total c2 = 0.278867E+14 jroot = 1 (1 = root found, 0 = no root)
t = 0.432E+05 no. steps = 379 order = 5 stepsize = 0.499E+03
c1 (bot.left/middle/top rt.) = 0.181E-07 0.331E-06 0.211E-07
c2 (bot.left/middle/top rt.) = 0.338E+12 0.136E+12 0.380E+12
total c2 = 0.287486E+14 jroot = 0 (1 = root found, 0 = no root)
t = 0.504E+05 no. steps = 401 order = 5 stepsize = 0.483E+03
c1 (bot.left/middle/top rt.) = 0.643E-08 0.423E-06 0.198E-07
c2 (bot.left/middle/top rt.) = 0.336E+12 0.493E+12 0.386E+12
total c2 = 0.361416E+14 jroot = 0 (1 = root found, 0 = no root)
t = 0.576E+05 no. steps = 414 order = 5 stepsize = 0.334E+03
c1 (bot.left/middle/top rt.) = -0.972E-11 -0.176E-09 0.200E-12
c2 (bot.left/middle/top rt.) = 0.332E+12 0.965E+12 0.391E+12
total c2 = 0.446354E+14 jroot = 0 (1 = root found, 0 = no root)
t = 0.648E+05 no. steps = 427 order = 5 stepsize = 0.789E+03
c1 (bot.left/middle/top rt.) = -0.987E-10 0.244E-08 -0.985E-10
c2 (bot.left/middle/top rt.) = 0.331E+12 0.892E+12 0.396E+12
total c2 = 0.492882E+14 jroot = 0 (1 = root found, 0 = no root)
t = 0.720E+05 no. steps = 436 order = 5 stepsize = 0.789E+03
c1 (bot.left/middle/top rt.) = 0.187E-11 0.395E-10 -0.109E-12
c2 (bot.left/middle/top rt.) = 0.333E+12 0.619E+12 0.404E+12
total c2 = 0.529683E+14 jroot = 0 (1 = root found, 0 = no root)
t = 0.792E+05 no. steps = 445 order = 5 stepsize = 0.789E+03
c1 (bot.left/middle/top rt.) = 0.794E-12 -0.147E-10 0.680E-12
c2 (bot.left/middle/top rt.) = 0.333E+12 0.667E+12 0.412E+12
total c2 = 0.605274E+14 jroot = 0 (1 = root found, 0 = no root)
t = 0.824E+05 no. steps = 449 order = 5 stepsize = 0.789E+03
c1 (bot.left/middle/top rt.) = -0.178E-12 0.308E-11 -0.148E-12
c2 (bot.left/middle/top rt.) = 0.334E+12 0.804E+12 0.415E+12
total c2 = 0.619212E+14 jroot = 1 (1 = root found, 0 = no root)
t = 0.864E+05 no. steps = 454 order = 5 stepsize = 0.789E+03
c1 (bot.left/middle/top rt.) = 0.157E-14 -0.419E-12 0.104E-13
c2 (bot.left/middle/top rt.) = 0.335E+12 0.911E+12 0.416E+12
total c2 = 0.597970E+14 jroot = 0 (1 = root found, 0 = no root)
Final statistics:
rwork size = 4264 iwork size = 230
number of steps = 454 no. fnal. iter. steps = 112
number of f evals. = 1547 number of g evals. = 504
number of prec. evals. = 52 number of Jac. evals. = 11
number of prec. solves = 1231
number of nonl. iters. = 461 number of lin. iters. = 847
average Krylov subspace dimension (nli/nni) = 1.8373
number of conv. failures: nonlinear = 0 linear = 0
==========Source and Output for LSODI Demonstration Program=====================
c-----------------------------------------------------------------------
c Demonstration program for the SLSODI package.
c This is the version of 12 June 2001.
c
c This version is in single precision.
c
C this program solves a semi-discretized form of the Burgers equation,
c
c u = -(u*u/2) + eta * u
c t x xx
c
c for a = -1 .le. x .le. 1 = b, t .ge. 0.
c Here eta = 0.05.
c Boundary conditions: u(-1,t) = u(1,t) = 0.
c Initial profile: square wave
c u(0,x) = 0 for 1/2 .lt. abs(x) .le. 1
c u(0,x) = 1/2 for abs(x) = 1/2
c u(0,x) = 1 for 0 .le. abs(x) .lt. 1/2
c
c An ODE system is generated by a simplified Galerkin treatment
c of the spatial variable x.
c
c Reference:
c R. C. Y. Chin, G. W. Hedstrom, and K. E. Karlsson,
c A Simplified Galerkin Method for Hyperbolic Equations,
c Math. Comp., vol. 33, no. 146 (April 1979), pp. 647-658.
c
c The problem is run with the SLSODI package with a 10-point mesh
c and a 100-point mesh. In each case, it is run with two tolerances
c and for various appropriate values of the method flag mf.
c Output is on unit lout, set to 6 in a data statement below.
c-----------------------------------------------------------------------
external res, addabd, addafl, jacbd, jacfl
integer i, io, istate, itol, iwork, j,
1 lout, liw, lrw, meth, miter, mf, ml, mu,
2 n, nout, npts, nerr,
3 nptsm1, n14, n34, n14m1, n14p1, n34m1, n34p1
integer nm1
real a, b, eta, delta,
1 zero, fourth, half, one, hun,
2 t, tout, tlast, tinit, errfac,
3 atol, rtol, rwork, y, ydoti, elkup
real eodsq, r4d
dimension y(99), ydoti(99), tout(4), atol(2), rtol(2)
dimension rwork(2002), iwork(125)
c Pass problem parameters in the Common block test1.
common /test1/ r4d, eodsq, nm1
c
c Set problem parameters and run parameters
data eta/0.05e0/, a/-1.0e0/, b/1.0e0/
data zero/0.0e0/, fourth/0.25e0/, half/.5e0/, one/1.0e0/,
1 hun/100.0e0/
data tinit/0.0e0/, tlast/0.4e0/
data tout/.10e0,.20e0,.30e0,.40e0/
data ml/1/, mu/1/, lout/6/
data nout/4/, lrw/2002/, liw/125/
data itol/1/, rtol/1.0e-3, 1.0e-6/, atol/1.0e-3, 1.0e-6/
c
iwork(1) = ml
iwork(2) = mu
nerr = 0
c
c Loop over two values of npts.
do 300 npts = 10, 100, 90
c
c Compute the mesh width delta and other parameters.
delta = (b - a)/npts
r4d = fourth/delta
eodsq = eta/delta**2
nptsm1 = npts - 1
n14 = npts/4
n34 = 3 * n14
n14m1 = n14 - 1
n14p1 = n14m1 + 2
n34m1 = n34 - 1
n34p1 = n34m1 + 2
n = nptsm1
nm1 = n - 1
c
c Set the initial profile (for output purposes only).
c
do 10 i = 1,n14m1
10 y(i) = zero
y(n14) = half
do 20 i = n14p1,n34m1
20 y(i) = one
y(n34) = half
do 30 i = n34p1,nptsm1
30 y(i) = zero
c
if (npts .gt. 10) write (lout,1010)
write (lout,1000)
write (lout,1100) eta,a,b,tinit,tlast,ml,mu,n
write (lout,1200) zero, (y(i), i=1,n), zero
c
c The j loop is over error tolerances.
c
do 200 j = 1,2
c
c Loop over method flag loop (for demonstration).
c
do 100 meth = 1,2
do 100 miter = 1,5
if (miter .eq. 3) go to 100
if (miter .le. 2 .and. npts .gt. 10) go to 100
if (miter .eq. 5 .and. npts .lt. 100) go to 100
mf = 10*meth + miter
c
c Set the initial profile.
c
do 40 i = 1,n14m1
40 y(i) = zero
y(n14) = half
do 50 i = n14p1,n34m1
50 y(i) = one
y(n34) = half
do 60 i = n34p1,nptsm1
60 y(i) = zero
c
t = tinit
istate = 0
c
write (lout,1500) rtol(j), atol(j), mf, npts
c
c Output loop for each case
c
do 80 io = 1,nout
c
c call SLSODI
if (miter .le. 2) call slsodi (res, addafl, jacfl, n, y,
1 ydoti, t, tout(io), itol, rtol(j), atol(j),
2 1, istate, 0, rwork, lrw, iwork, liw, mf)
if (miter .ge. 4) call slsodi (res, addabd, jacbd, n, y,
1 ydoti, t, tout(io), itol, rtol(j), atol(j),
2 1, istate, 0, rwork, lrw, iwork, liw, mf)
write (lout,2000) t, rwork(11), iwork(14),(y(i), i=1,n)
c
c If istate is not 2 on return, print message and loop.
if (istate .ne. 2) then
write (lout,4000) mf, t, istate
nerr = nerr + 1
go to 100
endif
c
80 continue
c
write (lout,3000) mf, iwork(11), iwork(12), iwork(13),
1 iwork(17), iwork(18)
c
c Estimate final error and print result.
errfac = elkup( n, y, rwork(21), itol, rtol(j), atol(j) )
if (errfac .gt. hun) then
write (lout,5001) errfac
nerr = nerr + 1
else
write (lout,5000) errfac
endif
100 continue
200 continue
300 continue
c
write (lout,6000) nerr
stop
c
1000 format(20x,' Demonstration Problem for SLSODI')
1010 format(///80('*')///)
1100 format(/10x,' Simplified Galerkin Solution of Burgers Equation'//
1 13x,'Diffusion coefficient is eta =',e10.2/
2 13x,'Uniform mesh on interval',e12.3,' to ',e12.3/
3 13x,'Zero boundary conditions'/
4 13x,'Time limits: t0 = ',e12.5,' tlast = ',e12.5/
5 13x,'Half-bandwidths ml = ',i2,' mu = ',i2/
6 13x,'System size neq = ',i3/)
c
1200 format('Initial profile:'/17(6e12.4/))
c
1500 format(///80('-')///'Run with rtol =',e12.2,' atol =',e12.2,
1 ' mf =',i3,' npts =',i4,':'//)
c
2000 format('Output for time t = ',e12.5,' current h =',
1 e12.5,' current order =',i2,':'/17(6e12.4/))
c
3000 format(//'Final statistics for mf = ',i2,':'/
1 i4,' steps,',i5,' res,',i4,' Jacobians,',
2 ' rwork size =',i6,', iwork size =',i6)
c
4000 format(///80('*')//20x,'Final time reached for mf = ',i2,
1 ' was t = ',e12.5/25x,'at which istate = ',i2////80('*'))
5000 format(' Final output is correct to within ',e8.1,
1 ' times local error tolerance')
5001 format(' Final output is wrong by ',e8.1,
1 ' times local error tolerance')
6000 format(//80('*')//
1 'Run completed. Number of errors encountered =',i3)
c
c end of main program for the SLSODI demonstration problem.
end
subroutine res (n, t, y, v, r, ires)
c This subroutine computes the residual vector
c r = g(t,y) - A(t,y)*v .
c It uses nm1 = n - 1 from Common.
c If ires = -1, only g(t,y) is returned in r, since A(t,y) does
c not depend on y.
c
integer i, ires, n, nm1
real t, y, v, r, r4d, eodsq, one, four, six,
1 fact1, fact4
dimension y(n), v(n), r(n)
common /test1/ r4d, eodsq, nm1
data one /1.0e0/, four /4.0e0/, six /6.0e0/
c
call gfun (n, t, y, r)
if (ires .eq. -1) return
c
fact1 = one/six
fact4 = four/six
r(1) = r(1) - (fact4*v(1) + fact1*v(2))
do 10 i = 2, nm1
10 r(i) = r(i) - (fact1*v(i-1) + fact4*v(i) + fact1*v(i+1))
r(n) = r(n) - (fact1*v(nm1) + fact4*v(n))
return
c end of subroutine res for the SLSODI demonstration problem.
end
subroutine gfun (n, t, y, g)
c This subroutine computes the right-hand side function g(y,t).
c It uses r4d = 1/(4*delta), eodsq = eta/delta**2, and nm1 = n - 1
c from the Common block test1.
c
integer i, n, nm1
real t, y, g, r4d, eodsq, two
dimension g(n), y(n)
common /test1/ r4d, eodsq, nm1
data two/2.0e0/
c
g(1) = -r4d*y(2)**2 + eodsq*(y(2) - two*y(1))
c
do 20 i = 2,nm1
g(i) = r4d*(y(i-1)**2 - y(i+1)**2)
1 + eodsq*(y(i+1) - two*y(i) + y(i-1))
20 continue
c
g(n) = r4d*y(nm1)**2 + eodsq*(y(nm1) - two*y(n))
c
return
c end of subroutine gfun for the SLSODI demonstration problem.
end
subroutine addabd (n, t, y, ml, mu, pa, m0)
c This subroutine computes the matrix A in band form, adds it to pa,
c and returns the sum in pa. The matrix A is tridiagonal, of order n,
c with nonzero elements (reading across) of 1/6, 4/6, 1/6.
c
integer i, n, m0, ml, mu, mup1, mup2
real t, y, pa, fact1, fact4, one, four, six
dimension y(n), pa(m0,n)
data one/1.0e0/, four/4.0e0/, six/6.0e0/
c
c Set the pointers.
mup1 = mu + 1
mup2 = mu + 2
c Compute the elements of A.
fact1 = one/six
fact4 = four/six
c Add the matrix A to the matrix pa (banded).
do 10 i = 1,n
pa(mu,i) = pa(mu,i) + fact1
pa(mup1,i) = pa(mup1,i) + fact4
pa(mup2,i) = pa(mup2,i) + fact1
10 continue
return
c end of subroutine addabd for the SLSODI demonstration problem.
end
subroutine addafl (n, t, y, ml, mu, pa, m0)
c This subroutine computes the matrix A in full form, adds it to
c pa, and returns the sum in pa.
c It uses nm1 = n - 1 from Common.
c The matrix A is tridiagonal, of order n, with nonzero elements
c (reading across) of 1/6, 4/6, 1/6.
c
integer i, n, m0, ml, mu, nm1
real t, y, pa, r4d, eodsq, one, four, six,
1 fact1, fact4
dimension y(n), pa(m0,n)
common /test1/ r4d, eodsq, nm1
data one/1.0e0/, four/4.0e0/, six/6.0e0/
c
c Compute the elements of A.
fact1 = one/six
fact4 = four/six
c
c Add the matrix A to the matrix pa (full).
c
do 110 i = 2, nm1
pa(i,i+1) = pa(i,i+1) + fact1
pa(i,i) = pa(i,i) + fact4
pa(i,i-1) = pa(i,i-1) + fact1
110 continue
pa(1,2) = pa(1,2) + fact1
pa(1,1) = pa(1,1) + fact4
pa(n,n) = pa(n,n) + fact4
pa(n,nm1) = pa(n,nm1) + fact1
return
c end of subroutine addafl for the SLSODI demonstration problem.
end
subroutine jacbd (n, t, y, s, ml, mu, pa, m0)
c This subroutine computes the Jacobian dg/dy = d(g-a*s)/dy
c and stores elements
c i j
c dg /dy in pa(i-j+mu+1,j) in band matrix format.
c It uses r4d = 1/(4*delta), eodsq = eta/delta**2, and nm1 = n - 1
c from the Common block test1.
c
integer i, n, m0, ml, mu, mup1, mup2, nm1
real t, y, s, pa, diag, r4d, eodsq, two, r2d
dimension y(n), s(n), pa(m0,n)
common /test1/ r4d, eodsq, nm1
data two/2.0e0/
c
mup1 = mu + 1
mup2 = mu + 2
diag = -two*eodsq
r2d = two*r4d
c 1 1
c Compute and store dg /dy
pa(mup1,1) = diag
c
c 1 2
c Compute and store dg /dy
pa(mu,2) = -r2d*y(2) + eodsq
c
do 20 i = 2,nm1
c
c i i-1
c Compute and store dg /dy
pa(mup2,i-1) = r2d*y(i-1) + eodsq
c
c i i
c Compute and store dg /dy
pa(mup1,i) = diag
c
c i i+1
c Compute and store dg /dy
pa(mu,i+1) = -r2d*y(i+1) + eodsq
20 continue
c
c n n-1
c Compute and store dg /dy
pa(mup2,nm1) = r2d*y(nm1) + eodsq
c
c n n
c Compute and store dg /dy
pa(mup1,n) = diag
c
return
c end of subroutine jacbd for the SLSODI demonstration problem.
end
subroutine jacfl (n, t, y, s, ml, mu, pa, m0)
c This subroutine computes the Jacobian dg/dy = d(g-a*s)/dy
c and stores elements
c i j
c dg /dy in pa(i,j) in full matrix format.
c It uses r4d = 1/(4*delta), eodsq = eta/delta**2, and nm1 = n - 1
c from the Common block test1.
c
integer i, n, m0, ml, mu, nm1
real t, y, s, pa, diag, r4d, eodsq, two, r2d
dimension y(n), s(n), pa(m0,n)
common /test1/ r4d, eodsq, nm1
data two/2.0e0/
c
diag = -two*eodsq
r2d = two*r4d
c
c 1 1
c Compute and store dg /dy
pa(1,1) = diag
c
c 1 2
c Compute and store dg /dy
pa(1,2) = -r2d*y(2) + eodsq
c
do 120 i = 2,nm1
c
c i i-1
c Compute and store dg /dy
pa(i,i-1) = r2d*y(i-1) + eodsq
c
c i i
c Compute and store dg /dy
pa(i,i) = diag
c
c i i+1
c Compute and store dg /dy
pa(i,i+1) = -r2d*y(i+1) + eodsq
120 continue
c
c n n-1
c Compute and store dg /dy
pa(n,nm1) = r2d*y(nm1) + eodsq
c
c n n
c Compute and store dg /dy
pa(n,n) = diag
c
return
c end of subroutine jacfl for the SLSODI demonstration problem.
end
real function elkup (n, y, ewt, itol, rtol, atol)
c This routine looks up approximately correct values of y at t = 0.4,
c ytrue = y9 or y99 depending on whether n = 9 or 99. These were
c obtained by running SLSODI with very tight tolerances.
c The returned value is
c elkup = norm of ( y - ytrue ) / ( rtol*abs(ytrue) + atol ).
c
integer n, itol, i
real y, ewt, rtol, atol, y9, y99, y99a, y99b, y99c,
1 y99d, y99e, y99f, y99g, svnorm
dimension y(n), ewt(n), y9(9), y99(99)
dimension y99a(16), y99b(16), y99c(16), y99d(16), y99e(16),
1 y99f(16), y99g(3)
equivalence (y99a(1),y99(1)), (y99b(1),y99(17)),
1 (y99c(1),y99(33)), (y99d(1),y99(49)), (y99e(1),y99(65)),
1 (y99f(1),y99(81)), (y99g(1),y99(97))
data y9 /
1 1.07001457e-01, 2.77432492e-01, 5.02444616e-01, 7.21037157e-01,
1 9.01670441e-01, 8.88832048e-01, 4.96572850e-01, 9.46924362e-02,
1-6.90855199e-03 /
data y99a /
1 2.05114384e-03, 4.19527452e-03, 6.52533872e-03, 9.13412751e-03,
1 1.21140191e-02, 1.55565301e-02, 1.95516488e-02, 2.41869487e-02,
1 2.95465081e-02, 3.57096839e-02, 4.27498067e-02, 5.07328729e-02,
1 5.97163151e-02, 6.97479236e-02, 8.08649804e-02, 9.30936515e-02 /
data y99b /
1 1.06448659e-01, 1.20933239e-01, 1.36539367e-01, 1.53248227e-01,
1 1.71030869e-01, 1.89849031e-01, 2.09656044e-01, 2.30397804e-01,
1 2.52013749e-01, 2.74437805e-01, 2.97599285e-01, 3.21423708e-01,
1 3.45833531e-01, 3.70748792e-01, 3.96087655e-01, 4.21766871e-01 /
data y99c /
1 4.47702161e-01, 4.73808532e-01, 5.00000546e-01, 5.26192549e-01,
1 5.52298887e-01, 5.78234121e-01, 6.03913258e-01, 6.29252015e-01,
1 6.54167141e-01, 6.78576790e-01, 7.02400987e-01, 7.25562165e-01,
1 7.47985803e-01, 7.69601151e-01, 7.90342031e-01, 8.10147715e-01 /
data y99d /
1 8.28963844e-01, 8.46743353e-01, 8.63447369e-01, 8.79046021e-01,
1 8.93519106e-01, 9.06856541e-01, 9.19058529e-01, 9.30135374e-01,
1 9.40106872e-01, 9.49001208e-01, 9.56853318e-01, 9.63702661e-01,
1 9.69590361e-01, 9.74555682e-01, 9.78631814e-01, 9.81840924e-01 /
data y99e /
1 9.84188430e-01, 9.85656465e-01, 9.86196496e-01, 9.85721098e-01,
1 9.84094964e-01, 9.81125395e-01, 9.76552747e-01, 9.70041743e-01,
1 9.61175143e-01, 9.49452051e-01, 9.34294085e-01, 9.15063568e-01,
1 8.91098383e-01, 8.61767660e-01, 8.26550038e-01, 7.85131249e-01 /
data y99f /
1 7.37510044e-01, 6.84092540e-01, 6.25748369e-01, 5.63802368e-01,
1 4.99946558e-01, 4.36077986e-01, 3.74091566e-01, 3.15672765e-01,
1 2.62134958e-01, 2.14330497e-01, 1.72640946e-01, 1.37031155e-01,
1 1.07140815e-01, 8.23867920e-02, 6.20562432e-02, 4.53794321e-02 /
data y99g / 3.15789227e-02, 1.98968820e-02, 9.60472135e-03 /
c
if (n .eq. 99) go to 99
c
c Compute local error tolerance using correct y (n = 9).
c
call sewset( n, itol, rtol, atol, y9, ewt )
c
c Invert ewt and replace y by the error, y - ytrue.
c
do 20 i = 1, 9
ewt(i) = 1.0e0/ewt(i)
20 y(i) = y(i) - y9(i)
go to 200
c
c Compute local error tolerance using correct y (n = 99).
c
99 call sewset( n, itol, rtol, atol, y99, ewt )
c
c Invert ewt and replace y by the error, y - ytrue.
c
do 120 i = 1, 99
ewt(i) = 1.0e0/ewt(i)
120 y(i) = y(i) - y99(i)
c
c Find weighted norm of the error and return.
c
200 elkup = svnorm (n, y, ewt)
return
c end of function elkup for the SLSODI demonstration program.
end
................................................................................
Demonstration Problem for DLSODI
Simplified Galerkin Solution of Burgers Equation
Diffusion coefficient is eta = 0.50E-01
Uniform mesh on interval -0.100E+01 to 0.100E+01
Zero boundary conditions
Time limits: t0 = 0.00000E+00 tlast = 0.40000E+00
Half-bandwidths ml = 1 mu = 1
System size neq = 9
Initial profile:
0.0000E+00 0.0000E+00 0.5000E+00 0.1000E+01 0.1000E+01 0.1000E+01
0.5000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
--------------------------------------------------------------------------------
Run with rtol = 0.10E-02 atol = 0.10E-02 mf = 11 npts = 10:
Output for time t = 0.10000E+00 current h = 0.42496E-01 current order = 2:
0.6081E-01 0.3900E+00 0.8101E+00 0.9897E+00 0.1013E+01 0.6407E+00
0.1147E+00 -0.1388E-01 0.1294E-02
Output for time t = 0.20000E+00 current h = 0.66617E-01 current order = 2:
0.8935E-01 0.3342E+00 0.6690E+00 0.9069E+00 0.1011E+01 0.7573E+00
0.2383E+00 -0.1250E-02 -0.3190E-02
Output for time t = 0.30000E+00 current h = 0.66617E-01 current order = 2:
0.1022E+00 0.3006E+00 0.5707E+00 0.8091E+00 0.9703E+00 0.8439E+00
0.3682E+00 0.3492E-01 -0.7198E-02
Output for time t = 0.40000E+00 current h = 0.98382E-01 current order = 2:
0.1073E+00 0.2768E+00 0.5009E+00 0.7212E+00 0.9043E+00 0.8896E+00
0.4949E+00 0.9423E-01 -0.6444E-02
Final statistics for mf = 11:
9 steps, 13 res, 4 Jacobians, rwork size = 247, iwork size = 29
Final output is correct to within 0.8E+00 times local error tolerance
--------------------------------------------------------------------------------
Run with rtol = 0.10E-02 atol = 0.10E-02 mf = 12 npts = 10:
Output for time t = 0.10000E+00 current h = 0.42496E-01 current order = 2:
0.6081E-01 0.3900E+00 0.8101E+00 0.9897E+00 0.1013E+01 0.6407E+00
0.1147E+00 -0.1388E-01 0.1294E-02
Output for time t = 0.20000E+00 current h = 0.66617E-01 current order = 2:
0.8935E-01 0.3342E+00 0.6690E+00 0.9069E+00 0.1011E+01 0.7573E+00
0.2383E+00 -0.1250E-02 -0.3190E-02
Output for time t = 0.30000E+00 current h = 0.66617E-01 current order = 2:
0.1022E+00 0.3006E+00 0.5707E+00 0.8091E+00 0.9703E+00 0.8439E+00
0.3682E+00 0.3492E-01 -0.7198E-02
Output for time t = 0.40000E+00 current h = 0.98382E-01 current order = 2:
0.1073E+00 0.2768E+00 0.5009E+00 0.7212E+00 0.9043E+00 0.8896E+00
0.4949E+00 0.9423E-01 -0.6444E-02
Final statistics for mf = 12:
9 steps, 53 res, 4 Jacobians, rwork size = 247, iwork size = 29
Final output is correct to within 0.8E+00 times local error tolerance
--------------------------------------------------------------------------------
Run with rtol = 0.10E-02 atol = 0.10E-02 mf = 14 npts = 10:
Output for time t = 0.10000E+00 current h = 0.42496E-01 current order = 2:
0.6081E-01 0.3900E+00 0.8101E+00 0.9897E+00 0.1013E+01 0.6407E+00
0.1147E+00 -0.1388E-01 0.1294E-02
Output for time t = 0.20000E+00 current h = 0.66617E-01 current order = 2:
0.8935E-01 0.3342E+00 0.6690E+00 0.9069E+00 0.1011E+01 0.7573E+00
0.2383E+00 -0.1250E-02 -0.3190E-02
Output for time t = 0.30000E+00 current h = 0.66617E-01 current order = 2:
0.1022E+00 0.3006E+00 0.5707E+00 0.8091E+00 0.9703E+00 0.8439E+00
0.3682E+00 0.3492E-01 -0.7198E-02
Output for time t = 0.40000E+00 current h = 0.98382E-01 current order = 2:
0.1073E+00 0.2768E+00 0.5009E+00 0.7212E+00 0.9043E+00 0.8896E+00
0.4949E+00 0.9423E-01 -0.6444E-02
Final statistics for mf = 14:
9 steps, 13 res, 4 Jacobians, rwork size = 202, iwork size = 29
Final output is correct to within 0.8E+00 times local error tolerance
--------------------------------------------------------------------------------
Run with rtol = 0.10E-02 atol = 0.10E-02 mf = 21 npts = 10:
Output for time t = 0.10000E+00 current h = 0.50696E-01 current order = 3:
0.6089E-01 0.3899E+00 0.8101E+00 0.9900E+00 0.1012E+01 0.6408E+00
0.1147E+00 -0.1391E-01 0.1328E-02
Output for time t = 0.20000E+00 current h = 0.50696E-01 current order = 3:
0.8864E-01 0.3358E+00 0.6687E+00 0.9046E+00 0.1013E+01 0.7569E+00
0.2384E+00 -0.1103E-02 -0.3436E-02
Output for time t = 0.30000E+00 current h = 0.57639E-01 current order = 3:
0.1014E+00 0.3024E+00 0.5717E+00 0.8058E+00 0.9704E+00 0.8448E+00
0.3684E+00 0.3507E-01 -0.7538E-02
Output for time t = 0.40000E+00 current h = 0.57639E-01 current order = 3:
0.1067E+00 0.2782E+00 0.5030E+00 0.7188E+00 0.9018E+00 0.8904E+00
0.4961E+00 0.9453E-01 -0.6919E-02
Final statistics for mf = 21:
11 steps, 14 res, 3 Jacobians, rwork size = 184, iwork size = 29
Final output is correct to within 0.6E+00 times local error tolerance
--------------------------------------------------------------------------------
Run with rtol = 0.10E-02 atol = 0.10E-02 mf = 22 npts = 10:
Output for time t = 0.10000E+00 current h = 0.50696E-01 current order = 3:
0.6089E-01 0.3899E+00 0.8101E+00 0.9900E+00 0.1012E+01 0.6408E+00
0.1147E+00 -0.1391E-01 0.1328E-02
Output for time t = 0.20000E+00 current h = 0.50696E-01 current order = 3:
0.8864E-01 0.3358E+00 0.6687E+00 0.9046E+00 0.1013E+01 0.7569E+00
0.2384E+00 -0.1103E-02 -0.3436E-02
Output for time t = 0.30000E+00 current h = 0.57639E-01 current order = 3:
0.1014E+00 0.3024E+00 0.5717E+00 0.8058E+00 0.9704E+00 0.8448E+00
0.3684E+00 0.3507E-01 -0.7538E-02
Output for time t = 0.40000E+00 current h = 0.57639E-01 current order = 3:
0.1067E+00 0.2782E+00 0.5030E+00 0.7188E+00 0.9018E+00 0.8904E+00
0.4961E+00 0.9453E-01 -0.6919E-02
Final statistics for mf = 22:
11 steps, 44 res, 3 Jacobians, rwork size = 184, iwork size = 29
Final output is correct to within 0.6E+00 times local error tolerance
--------------------------------------------------------------------------------
Run with rtol = 0.10E-02 atol = 0.10E-02 mf = 24 npts = 10:
Output for time t = 0.10000E+00 current h = 0.50696E-01 current order = 3:
0.6089E-01 0.3899E+00 0.8101E+00 0.9900E+00 0.1012E+01 0.6408E+00
0.1147E+00 -0.1391E-01 0.1328E-02
Output for time t = 0.20000E+00 current h = 0.50696E-01 current order = 3:
0.8864E-01 0.3358E+00 0.6687E+00 0.9046E+00 0.1013E+01 0.7569E+00
0.2384E+00 -0.1103E-02 -0.3436E-02
Output for time t = 0.30000E+00 current h = 0.57639E-01 current order = 3:
0.1014E+00 0.3024E+00 0.5717E+00 0.8058E+00 0.9704E+00 0.8448E+00
0.3684E+00 0.3507E-01 -0.7538E-02
Output for time t = 0.40000E+00 current h = 0.57639E-01 current order = 3:
0.1067E+00 0.2782E+00 0.5030E+00 0.7188E+00 0.9018E+00 0.8904E+00
0.4961E+00 0.9453E-01 -0.6919E-02
Final statistics for mf = 24:
11 steps, 14 res, 3 Jacobians, rwork size = 139, iwork size = 29
Final output is correct to within 0.6E+00 times local error tolerance
--------------------------------------------------------------------------------
Run with rtol = 0.10E-05 atol = 0.10E-05 mf = 11 npts = 10:
Output for time t = 0.10000E+00 current h = 0.16073E-01 current order = 4:
0.6054E-01 0.3907E+00 0.8099E+00 0.9886E+00 0.1013E+01 0.6407E+00
0.1147E+00 -0.1382E-01 0.1185E-02
Output for time t = 0.20000E+00 current h = 0.24112E-01 current order = 5:
0.8890E-01 0.3352E+00 0.6696E+00 0.9050E+00 0.1011E+01 0.7581E+00
0.2384E+00 -0.1212E-02 -0.3381E-02
Output for time t = 0.30000E+00 current h = 0.33274E-01 current order = 5:
0.1018E+00 0.3014E+00 0.5720E+00 0.8078E+00 0.9686E+00 0.8445E+00
0.3690E+00 0.3491E-01 -0.7446E-02
Output for time t = 0.40000E+00 current h = 0.33274E-01 current order = 5:
0.1070E+00 0.2774E+00 0.5024E+00 0.7210E+00 0.9017E+00 0.8888E+00
0.4966E+00 0.9469E-01 -0.6909E-02
Final statistics for mf = 11:
24 steps, 32 res, 6 Jacobians, rwork size = 247, iwork size = 29
Final output is correct to within 0.4E+00 times local error tolerance
--------------------------------------------------------------------------------
Run with rtol = 0.10E-05 atol = 0.10E-05 mf = 12 npts = 10:
Output for time t = 0.10000E+00 current h = 0.16073E-01 current order = 4:
0.6054E-01 0.3907E+00 0.8099E+00 0.9886E+00 0.1013E+01 0.6407E+00
0.1147E+00 -0.1382E-01 0.1185E-02
Output for time t = 0.20000E+00 current h = 0.24112E-01 current order = 5:
0.8890E-01 0.3352E+00 0.6696E+00 0.9050E+00 0.1011E+01 0.7581E+00
0.2384E+00 -0.1212E-02 -0.3381E-02
Output for time t = 0.30000E+00 current h = 0.33274E-01 current order = 5:
0.1018E+00 0.3014E+00 0.5720E+00 0.8078E+00 0.9686E+00 0.8445E+00
0.3690E+00 0.3491E-01 -0.7446E-02
Output for time t = 0.40000E+00 current h = 0.33274E-01 current order = 5:
0.1070E+00 0.2774E+00 0.5024E+00 0.7210E+00 0.9017E+00 0.8888E+00
0.4966E+00 0.9469E-01 -0.6909E-02
Final statistics for mf = 12:
24 steps, 92 res, 6 Jacobians, rwork size = 247, iwork size = 29
Final output is correct to within 0.4E+00 times local error tolerance
--------------------------------------------------------------------------------
Run with rtol = 0.10E-05 atol = 0.10E-05 mf = 14 npts = 10:
Output for time t = 0.10000E+00 current h = 0.16073E-01 current order = 4:
0.6054E-01 0.3907E+00 0.8099E+00 0.9886E+00 0.1013E+01 0.6407E+00
0.1147E+00 -0.1382E-01 0.1185E-02
Output for time t = 0.20000E+00 current h = 0.24112E-01 current order = 5:
0.8890E-01 0.3352E+00 0.6696E+00 0.9050E+00 0.1011E+01 0.7581E+00
0.2384E+00 -0.1212E-02 -0.3381E-02
Output for time t = 0.30000E+00 current h = 0.33274E-01 current order = 5:
0.1018E+00 0.3014E+00 0.5720E+00 0.8078E+00 0.9686E+00 0.8445E+00
0.3690E+00 0.3491E-01 -0.7446E-02
Output for time t = 0.40000E+00 current h = 0.33274E-01 current order = 5:
0.1070E+00 0.2774E+00 0.5024E+00 0.7210E+00 0.9017E+00 0.8888E+00
0.4966E+00 0.9469E-01 -0.6909E-02
Final statistics for mf = 14:
24 steps, 32 res, 6 Jacobians, rwork size = 202, iwork size = 29
Final output is correct to within 0.4E+00 times local error tolerance
--------------------------------------------------------------------------------
Run with rtol = 0.10E-05 atol = 0.10E-05 mf = 21 npts = 10:
Output for time t = 0.10000E+00 current h = 0.10895E-01 current order = 4:
0.6054E-01 0.3907E+00 0.8099E+00 0.9886E+00 0.1013E+01 0.6407E+00
0.1147E+00 -0.1382E-01 0.1185E-02
Output for time t = 0.20000E+00 current h = 0.16165E-01 current order = 5:
0.8890E-01 0.3352E+00 0.6696E+00 0.9050E+00 0.1011E+01 0.7581E+00
0.2384E+00 -0.1212E-02 -0.3381E-02
Output for time t = 0.30000E+00 current h = 0.26124E-01 current order = 5:
0.1018E+00 0.3014E+00 0.5720E+00 0.8078E+00 0.9686E+00 0.8445E+00
0.3690E+00 0.3491E-01 -0.7446E-02
Output for time t = 0.40000E+00 current h = 0.26124E-01 current order = 5:
0.1070E+00 0.2774E+00 0.5024E+00 0.7210E+00 0.9017E+00 0.8888E+00
0.4966E+00 0.9469E-01 -0.6909E-02
Final statistics for mf = 21:
35 steps, 44 res, 7 Jacobians, rwork size = 184, iwork size = 29
Final output is correct to within 0.1E+01 times local error tolerance
--------------------------------------------------------------------------------
Run with rtol = 0.10E-05 atol = 0.10E-05 mf = 22 npts = 10:
Output for time t = 0.10000E+00 current h = 0.10895E-01 current order = 4:
0.6054E-01 0.3907E+00 0.8099E+00 0.9886E+00 0.1013E+01 0.6407E+00
0.1147E+00 -0.1382E-01 0.1185E-02
Output for time t = 0.20000E+00 current h = 0.16165E-01 current order = 5:
0.8890E-01 0.3352E+00 0.6696E+00 0.9050E+00 0.1011E+01 0.7581E+00
0.2384E+00 -0.1212E-02 -0.3381E-02
Output for time t = 0.30000E+00 current h = 0.26124E-01 current order = 5:
0.1018E+00 0.3014E+00 0.5720E+00 0.8078E+00 0.9686E+00 0.8445E+00
0.3690E+00 0.3491E-01 -0.7446E-02
Output for time t = 0.40000E+00 current h = 0.26124E-01 current order = 5:
0.1070E+00 0.2774E+00 0.5024E+00 0.7210E+00 0.9017E+00 0.8888E+00
0.4966E+00 0.9469E-01 -0.6909E-02
Final statistics for mf = 22:
35 steps, 114 res, 7 Jacobians, rwork size = 184, iwork size = 29
Final output is correct to within 0.1E+01 times local error tolerance
--------------------------------------------------------------------------------
Run with rtol = 0.10E-05 atol = 0.10E-05 mf = 24 npts = 10:
Output for time t = 0.10000E+00 current h = 0.10895E-01 current order = 4:
0.6054E-01 0.3907E+00 0.8099E+00 0.9886E+00 0.1013E+01 0.6407E+00
0.1147E+00 -0.1382E-01 0.1185E-02
Output for time t = 0.20000E+00 current h = 0.16165E-01 current order = 5:
0.8890E-01 0.3352E+00 0.6696E+00 0.9050E+00 0.1011E+01 0.7581E+00
0.2384E+00 -0.1212E-02 -0.3381E-02
Output for time t = 0.30000E+00 current h = 0.26124E-01 current order = 5:
0.1018E+00 0.3014E+00 0.5720E+00 0.8078E+00 0.9686E+00 0.8445E+00
0.3690E+00 0.3491E-01 -0.7446E-02
Output for time t = 0.40000E+00 current h = 0.26124E-01 current order = 5:
0.1070E+00 0.2774E+00 0.5024E+00 0.7210E+00 0.9017E+00 0.8888E+00
0.4966E+00 0.9469E-01 -0.6909E-02
Final statistics for mf = 24:
35 steps, 44 res, 7 Jacobians, rwork size = 139, iwork size = 29
Final output is correct to within 0.1E+01 times local error tolerance
********************************************************************************
Demonstration Problem for DLSODI
Simplified Galerkin Solution of Burgers Equation
Diffusion coefficient is eta = 0.50E-01
Uniform mesh on interval -0.100E+01 to 0.100E+01
Zero boundary conditions
Time limits: t0 = 0.00000E+00 tlast = 0.40000E+00
Half-bandwidths ml = 1 mu = 1
System size neq = 99
Initial profile:
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.5000E+00 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.1000E+01 0.1000E+01 0.1000E+01 0.5000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
--------------------------------------------------------------------------------
Run with rtol = 0.10E-02 atol = 0.10E-02 mf = 14 npts = 100:
Output for time t = 0.10000E+00 current h = 0.32596E-01 current order = 2:
0.8566E-06 0.2312E-05 0.5353E-05 0.1197E-04 0.2629E-04 0.5678E-04
0.1203E-03 0.2492E-03 0.5031E-03 0.9860E-03 0.1869E-02 0.3419E-02
0.6021E-02 0.1020E-01 0.1661E-01 0.2604E-01 0.3930E-01 0.5724E-01
0.8055E-01 0.1098E+00 0.1452E+00 0.1869E+00 0.2344E+00 0.2872E+00
0.3444E+00 0.4050E+00 0.4676E+00 0.5310E+00 0.5938E+00 0.6547E+00
0.7123E+00 0.7656E+00 0.8136E+00 0.8556E+00 0.8913E+00 0.9206E+00
0.9437E+00 0.9614E+00 0.9743E+00 0.9835E+00 0.9896E+00 0.9937E+00
0.9963E+00 0.9978E+00 0.9988E+00 0.9993E+00 0.9996E+00 0.9998E+00
0.9999E+00 0.9999E+00 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.9999E+00 0.9998E+00 0.9996E+00 0.9992E+00 0.9983E+00 0.9966E+00
0.9935E+00 0.9881E+00 0.9791E+00 0.9647E+00 0.9427E+00 0.9107E+00
0.8661E+00 0.8071E+00 0.7334E+00 0.6464E+00 0.5502E+00 0.4506E+00
0.3541E+00 0.2668E+00 0.1928E+00 0.1336E+00 0.8887E-01 0.5683E-01
0.3497E-01 0.2071E-01 0.1183E-01 0.6516E-02 0.3469E-02 0.1789E-02
0.8957E-03 0.4369E-03 0.2082E-03 0.9727E-04 0.4467E-04 0.2021E-04
0.8997E-05 0.3873E-05 0.1432E-05
Output for time t = 0.20000E+00 current h = 0.57739E-01 current order = 2:
0.1580E-03 0.3506E-03 0.6171E-03 0.1007E-02 0.1584E-02 0.2433E-02
0.3662E-02 0.5405E-02 0.7830E-02 0.1113E-01 0.1553E-01 0.2126E-01
0.2858E-01 0.3774E-01 0.4899E-01 0.6253E-01 0.7855E-01 0.9717E-01
0.1185E+00 0.1425E+00 0.1692E+00 0.1984E+00 0.2301E+00 0.2641E+00
0.3000E+00 0.3377E+00 0.3767E+00 0.4169E+00 0.4578E+00 0.4991E+00
0.5405E+00 0.5815E+00 0.6219E+00 0.6613E+00 0.6993E+00 0.7357E+00
0.7700E+00 0.8022E+00 0.8319E+00 0.8589E+00 0.8831E+00 0.9045E+00
0.9230E+00 0.9389E+00 0.9521E+00 0.9631E+00 0.9719E+00 0.9789E+00
0.9844E+00 0.9886E+00 0.9917E+00 0.9941E+00 0.9958E+00 0.9971E+00
0.9980E+00 0.9986E+00 0.9990E+00 0.9993E+00 0.9994E+00 0.9994E+00
0.9993E+00 0.9990E+00 0.9985E+00 0.9976E+00 0.9961E+00 0.9939E+00
0.9905E+00 0.9855E+00 0.9782E+00 0.9679E+00 0.9535E+00 0.9341E+00
0.9082E+00 0.8748E+00 0.8328E+00 0.7816E+00 0.7213E+00 0.6528E+00
0.5782E+00 0.5002E+00 0.4222E+00 0.3475E+00 0.2789E+00 0.2184E+00
0.1671E+00 0.1249E+00 0.9146E-01 0.6562E-01 0.4617E-01 0.3190E-01
0.2165E-01 0.1444E-01 0.9475E-02 0.6114E-02 0.3877E-02 0.2407E-02
0.1446E-02 0.8090E-03 0.3610E-03
Output for time t = 0.30000E+00 current h = 0.57739E-01 current order = 2:
0.9060E-03 0.1896E-02 0.3055E-02 0.4476E-02 0.6255E-02 0.8498E-02
0.1132E-01 0.1483E-01 0.1916E-01 0.2444E-01 0.3078E-01 0.3832E-01
0.4715E-01 0.5739E-01 0.6911E-01 0.8238E-01 0.9724E-01 0.1137E+00
0.1318E+00 0.1515E+00 0.1728E+00 0.1955E+00 0.2197E+00 0.2452E+00
0.2720E+00 0.2998E+00 0.3287E+00 0.3584E+00 0.3888E+00 0.4197E+00
0.4511E+00 0.4828E+00 0.5146E+00 0.5464E+00 0.5779E+00 0.6092E+00
0.6399E+00 0.6700E+00 0.6993E+00 0.7277E+00 0.7549E+00 0.7810E+00
0.8056E+00 0.8288E+00 0.8505E+00 0.8704E+00 0.8887E+00 0.9052E+00
0.9200E+00 0.9330E+00 0.9444E+00 0.9543E+00 0.9627E+00 0.9699E+00
0.9758E+00 0.9807E+00 0.9847E+00 0.9879E+00 0.9904E+00 0.9923E+00
0.9937E+00 0.9947E+00 0.9951E+00 0.9950E+00 0.9944E+00 0.9931E+00
0.9910E+00 0.9878E+00 0.9831E+00 0.9767E+00 0.9679E+00 0.9561E+00
0.9407E+00 0.9207E+00 0.8954E+00 0.8639E+00 0.8255E+00 0.7799E+00
0.7270E+00 0.6676E+00 0.6028E+00 0.5346E+00 0.4652E+00 0.3970E+00
0.3322E+00 0.2728E+00 0.2200E+00 0.1743E+00 0.1359E+00 0.1043E+00
0.7895E-01 0.5891E-01 0.4336E-01 0.3144E-01 0.2240E-01 0.1557E-01
0.1037E-01 0.6312E-02 0.2981E-02
Output for time t = 0.40000E+00 current h = 0.90345E-01 current order = 2:
0.2030E-02 0.4154E-02 0.6468E-02 0.9065E-02 0.1204E-01 0.1548E-01
0.1949E-01 0.2414E-01 0.2952E-01 0.3572E-01 0.4279E-01 0.5081E-01
0.5982E-01 0.6989E-01 0.8103E-01 0.9327E-01 0.1066E+00 0.1211E+00
0.1367E+00 0.1534E+00 0.1711E+00 0.1899E+00 0.2096E+00 0.2302E+00
0.2518E+00 0.2741E+00 0.2971E+00 0.3208E+00 0.3451E+00 0.3700E+00
0.3952E+00 0.4208E+00 0.4466E+00 0.4726E+00 0.4988E+00 0.5249E+00
0.5511E+00 0.5770E+00 0.6028E+00 0.6283E+00 0.6533E+00 0.6780E+00
0.7020E+00 0.7255E+00 0.7482E+00 0.7702E+00 0.7913E+00 0.8114E+00
0.8305E+00 0.8486E+00 0.8655E+00 0.8812E+00 0.8958E+00 0.9091E+00
0.9212E+00 0.9321E+00 0.9419E+00 0.9505E+00 0.9581E+00 0.9646E+00
0.9702E+00 0.9749E+00 0.9787E+00 0.9816E+00 0.9838E+00 0.9851E+00
0.9855E+00 0.9849E+00 0.9833E+00 0.9803E+00 0.9758E+00 0.9694E+00
0.9606E+00 0.9490E+00 0.9340E+00 0.9149E+00 0.8910E+00 0.8618E+00
0.8266E+00 0.7851E+00 0.7374E+00 0.6838E+00 0.6252E+00 0.5632E+00
0.4992E+00 0.4353E+00 0.3734E+00 0.3150E+00 0.2615E+00 0.2138E+00
0.1722E+00 0.1367E+00 0.1069E+00 0.8223E-01 0.6196E-01 0.4533E-01
0.3156E-01 0.1989E-01 0.9605E-02
Final statistics for mf = 14:
27 steps, 40 res, 11 Jacobians, rwork size = 2002, iwork size = 119
Final output is correct to within 0.5E+00 times local error tolerance
--------------------------------------------------------------------------------
Run with rtol = 0.10E-02 atol = 0.10E-02 mf = 15 npts = 100:
Output for time t = 0.10000E+00 current h = 0.32596E-01 current order = 2:
0.8566E-06 0.2312E-05 0.5353E-05 0.1197E-04 0.2629E-04 0.5678E-04
0.1203E-03 0.2492E-03 0.5031E-03 0.9860E-03 0.1869E-02 0.3419E-02
0.6021E-02 0.1020E-01 0.1661E-01 0.2604E-01 0.3930E-01 0.5724E-01
0.8055E-01 0.1098E+00 0.1452E+00 0.1869E+00 0.2344E+00 0.2872E+00
0.3444E+00 0.4050E+00 0.4676E+00 0.5310E+00 0.5938E+00 0.6547E+00
0.7123E+00 0.7656E+00 0.8136E+00 0.8556E+00 0.8913E+00 0.9206E+00
0.9437E+00 0.9614E+00 0.9743E+00 0.9835E+00 0.9896E+00 0.9937E+00
0.9963E+00 0.9978E+00 0.9988E+00 0.9993E+00 0.9996E+00 0.9998E+00
0.9999E+00 0.9999E+00 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.9999E+00 0.9998E+00 0.9996E+00 0.9992E+00 0.9983E+00 0.9966E+00
0.9935E+00 0.9881E+00 0.9791E+00 0.9647E+00 0.9427E+00 0.9107E+00
0.8661E+00 0.8071E+00 0.7334E+00 0.6464E+00 0.5502E+00 0.4506E+00
0.3541E+00 0.2668E+00 0.1928E+00 0.1336E+00 0.8887E-01 0.5683E-01
0.3497E-01 0.2071E-01 0.1183E-01 0.6516E-02 0.3469E-02 0.1789E-02
0.8957E-03 0.4369E-03 0.2082E-03 0.9727E-04 0.4467E-04 0.2021E-04
0.8997E-05 0.3873E-05 0.1432E-05
Output for time t = 0.20000E+00 current h = 0.57739E-01 current order = 2:
0.1580E-03 0.3506E-03 0.6171E-03 0.1007E-02 0.1584E-02 0.2433E-02
0.3662E-02 0.5405E-02 0.7830E-02 0.1113E-01 0.1553E-01 0.2126E-01
0.2858E-01 0.3774E-01 0.4899E-01 0.6253E-01 0.7855E-01 0.9717E-01
0.1185E+00 0.1425E+00 0.1692E+00 0.1984E+00 0.2301E+00 0.2641E+00
0.3000E+00 0.3377E+00 0.3767E+00 0.4169E+00 0.4578E+00 0.4991E+00
0.5405E+00 0.5815E+00 0.6219E+00 0.6613E+00 0.6993E+00 0.7357E+00
0.7700E+00 0.8022E+00 0.8319E+00 0.8589E+00 0.8831E+00 0.9045E+00
0.9230E+00 0.9389E+00 0.9521E+00 0.9631E+00 0.9719E+00 0.9789E+00
0.9844E+00 0.9886E+00 0.9917E+00 0.9941E+00 0.9958E+00 0.9971E+00
0.9980E+00 0.9986E+00 0.9990E+00 0.9993E+00 0.9994E+00 0.9994E+00
0.9993E+00 0.9990E+00 0.9985E+00 0.9976E+00 0.9961E+00 0.9939E+00
0.9905E+00 0.9855E+00 0.9782E+00 0.9679E+00 0.9535E+00 0.9341E+00
0.9082E+00 0.8748E+00 0.8328E+00 0.7816E+00 0.7213E+00 0.6528E+00
0.5782E+00 0.5002E+00 0.4222E+00 0.3475E+00 0.2789E+00 0.2184E+00
0.1671E+00 0.1249E+00 0.9146E-01 0.6562E-01 0.4617E-01 0.3190E-01
0.2165E-01 0.1444E-01 0.9475E-02 0.6114E-02 0.3877E-02 0.2407E-02
0.1446E-02 0.8090E-03 0.3610E-03
Output for time t = 0.30000E+00 current h = 0.57739E-01 current order = 2:
0.9060E-03 0.1896E-02 0.3055E-02 0.4476E-02 0.6255E-02 0.8498E-02
0.1132E-01 0.1483E-01 0.1916E-01 0.2444E-01 0.3078E-01 0.3832E-01
0.4715E-01 0.5739E-01 0.6911E-01 0.8238E-01 0.9724E-01 0.1137E+00
0.1318E+00 0.1515E+00 0.1728E+00 0.1955E+00 0.2197E+00 0.2452E+00
0.2720E+00 0.2998E+00 0.3287E+00 0.3584E+00 0.3888E+00 0.4197E+00
0.4511E+00 0.4828E+00 0.5146E+00 0.5464E+00 0.5779E+00 0.6092E+00
0.6399E+00 0.6700E+00 0.6993E+00 0.7277E+00 0.7549E+00 0.7810E+00
0.8056E+00 0.8288E+00 0.8505E+00 0.8704E+00 0.8887E+00 0.9052E+00
0.9200E+00 0.9330E+00 0.9444E+00 0.9543E+00 0.9627E+00 0.9699E+00
0.9758E+00 0.9807E+00 0.9847E+00 0.9879E+00 0.9904E+00 0.9923E+00
0.9937E+00 0.9947E+00 0.9951E+00 0.9950E+00 0.9944E+00 0.9931E+00
0.9910E+00 0.9878E+00 0.9831E+00 0.9767E+00 0.9679E+00 0.9561E+00
0.9407E+00 0.9207E+00 0.8954E+00 0.8639E+00 0.8255E+00 0.7799E+00
0.7270E+00 0.6676E+00 0.6028E+00 0.5346E+00 0.4652E+00 0.3970E+00
0.3322E+00 0.2728E+00 0.2200E+00 0.1743E+00 0.1359E+00 0.1043E+00
0.7895E-01 0.5891E-01 0.4336E-01 0.3144E-01 0.2240E-01 0.1557E-01
0.1037E-01 0.6312E-02 0.2981E-02
Output for time t = 0.40000E+00 current h = 0.90345E-01 current order = 2:
0.2030E-02 0.4154E-02 0.6468E-02 0.9065E-02 0.1204E-01 0.1548E-01
0.1949E-01 0.2414E-01 0.2952E-01 0.3572E-01 0.4279E-01 0.5081E-01
0.5982E-01 0.6989E-01 0.8103E-01 0.9327E-01 0.1066E+00 0.1211E+00
0.1367E+00 0.1534E+00 0.1711E+00 0.1899E+00 0.2096E+00 0.2302E+00
0.2518E+00 0.2741E+00 0.2971E+00 0.3208E+00 0.3451E+00 0.3700E+00
0.3952E+00 0.4208E+00 0.4466E+00 0.4726E+00 0.4988E+00 0.5249E+00
0.5511E+00 0.5770E+00 0.6028E+00 0.6283E+00 0.6533E+00 0.6780E+00
0.7020E+00 0.7255E+00 0.7482E+00 0.7702E+00 0.7913E+00 0.8114E+00
0.8305E+00 0.8486E+00 0.8655E+00 0.8812E+00 0.8958E+00 0.9091E+00
0.9212E+00 0.9321E+00 0.9419E+00 0.9505E+00 0.9581E+00 0.9646E+00
0.9702E+00 0.9749E+00 0.9787E+00 0.9816E+00 0.9838E+00 0.9851E+00
0.9855E+00 0.9849E+00 0.9833E+00 0.9803E+00 0.9758E+00 0.9694E+00
0.9606E+00 0.9490E+00 0.9340E+00 0.9149E+00 0.8910E+00 0.8618E+00
0.8266E+00 0.7851E+00 0.7374E+00 0.6838E+00 0.6252E+00 0.5632E+00
0.4992E+00 0.4353E+00 0.3734E+00 0.3150E+00 0.2615E+00 0.2138E+00
0.1722E+00 0.1367E+00 0.1069E+00 0.8223E-01 0.6196E-01 0.4533E-01
0.3156E-01 0.1989E-01 0.9605E-02
Final statistics for mf = 15:
27 steps, 84 res, 11 Jacobians, rwork size = 2002, iwork size = 119
Final output is correct to within 0.5E+00 times local error tolerance
--------------------------------------------------------------------------------
Run with rtol = 0.10E-02 atol = 0.10E-02 mf = 24 npts = 100:
Output for time t = 0.10000E+00 current h = 0.20794E-01 current order = 3:
0.8937E-06 0.2397E-05 0.5502E-05 0.1218E-04 0.2650E-04 0.5674E-04
0.1194E-03 0.2461E-03 0.4957E-03 0.9720E-03 0.1849E-02 0.3399E-02
0.6018E-02 0.1023E-01 0.1670E-01 0.2616E-01 0.3942E-01 0.5730E-01
0.8054E-01 0.1097E+00 0.1451E+00 0.1867E+00 0.2342E+00 0.2871E+00
0.3445E+00 0.4053E+00 0.4681E+00 0.5315E+00 0.5942E+00 0.6550E+00
0.7124E+00 0.7654E+00 0.8131E+00 0.8550E+00 0.8907E+00 0.9202E+00
0.9436E+00 0.9615E+00 0.9745E+00 0.9837E+00 0.9898E+00 0.9938E+00
0.9963E+00 0.9978E+00 0.9988E+00 0.9993E+00 0.9996E+00 0.9998E+00
0.9999E+00 0.9999E+00 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.9999E+00 0.9998E+00 0.9996E+00 0.9992E+00 0.9983E+00 0.9966E+00
0.9935E+00 0.9881E+00 0.9791E+00 0.9648E+00 0.9428E+00 0.9109E+00
0.8663E+00 0.8073E+00 0.7333E+00 0.6462E+00 0.5499E+00 0.4503E+00
0.3540E+00 0.2668E+00 0.1928E+00 0.1337E+00 0.8901E-01 0.5693E-01
0.3500E-01 0.2069E-01 0.1177E-01 0.6463E-02 0.3431E-02 0.1767E-02
0.8858E-03 0.4335E-03 0.2078E-03 0.9780E-04 0.4530E-04 0.2068E-04
0.9287E-05 0.4027E-05 0.1497E-05
Output for time t = 0.20000E+00 current h = 0.28924E-01 current order = 2:
0.1546E-03 0.3436E-03 0.6066E-03 0.9934E-03 0.1569E-02 0.2420E-02
0.3656E-02 0.5415E-02 0.7865E-02 0.1120E-01 0.1563E-01 0.2140E-01
0.2874E-01 0.3789E-01 0.4909E-01 0.6256E-01 0.7848E-01 0.9700E-01
0.1182E+00 0.1422E+00 0.1689E+00 0.1982E+00 0.2300E+00 0.2641E+00
0.3003E+00 0.3381E+00 0.3774E+00 0.4178E+00 0.4588E+00 0.5002E+00
0.5415E+00 0.5823E+00 0.6223E+00 0.6613E+00 0.6988E+00 0.7348E+00
0.7688E+00 0.8008E+00 0.8305E+00 0.8576E+00 0.8821E+00 0.9038E+00
0.9227E+00 0.9388E+00 0.9523E+00 0.9633E+00 0.9722E+00 0.9793E+00
0.9847E+00 0.9889E+00 0.9920E+00 0.9943E+00 0.9960E+00 0.9972E+00
0.9980E+00 0.9986E+00 0.9990E+00 0.9993E+00 0.9994E+00 0.9994E+00
0.9993E+00 0.9990E+00 0.9985E+00 0.9976E+00 0.9961E+00 0.9939E+00
0.9905E+00 0.9856E+00 0.9784E+00 0.9681E+00 0.9538E+00 0.9343E+00
0.9084E+00 0.8749E+00 0.8328E+00 0.7814E+00 0.7210E+00 0.6524E+00
0.5778E+00 0.4999E+00 0.4220E+00 0.3475E+00 0.2790E+00 0.2186E+00
0.1673E+00 0.1251E+00 0.9161E-01 0.6570E-01 0.4620E-01 0.3187E-01
0.2159E-01 0.1436E-01 0.9396E-02 0.6043E-02 0.3819E-02 0.2363E-02
0.1416E-02 0.7900E-03 0.3520E-03
Output for time t = 0.30000E+00 current h = 0.49754E-01 current order = 3:
0.9126E-03 0.1910E-02 0.3079E-02 0.4512E-02 0.6305E-02 0.8562E-02
0.1139E-01 0.1492E-01 0.1925E-01 0.2452E-01 0.3085E-01 0.3836E-01
0.4716E-01 0.5736E-01 0.6904E-01 0.8227E-01 0.9710E-01 0.1136E+00
0.1316E+00 0.1514E+00 0.1726E+00 0.1955E+00 0.2197E+00 0.2454E+00
0.2722E+00 0.3002E+00 0.3292E+00 0.3590E+00 0.3895E+00 0.4205E+00
0.4520E+00 0.4836E+00 0.5154E+00 0.5471E+00 0.5786E+00 0.6097E+00
0.6402E+00 0.6700E+00 0.6991E+00 0.7271E+00 0.7541E+00 0.7799E+00
0.8044E+00 0.8276E+00 0.8492E+00 0.8692E+00 0.8876E+00 0.9043E+00
0.9193E+00 0.9325E+00 0.9441E+00 0.9542E+00 0.9627E+00 0.9700E+00
0.9760E+00 0.9809E+00 0.9850E+00 0.9882E+00 0.9907E+00 0.9926E+00
0.9940E+00 0.9949E+00 0.9953E+00 0.9953E+00 0.9946E+00 0.9933E+00
0.9912E+00 0.9879E+00 0.9833E+00 0.9769E+00 0.9681E+00 0.9563E+00
0.9408E+00 0.9208E+00 0.8954E+00 0.8638E+00 0.8253E+00 0.7796E+00
0.7268E+00 0.6674E+00 0.6027E+00 0.5346E+00 0.4653E+00 0.3972E+00
0.3325E+00 0.2731E+00 0.2202E+00 0.1745E+00 0.1360E+00 0.1044E+00
0.7900E-01 0.5892E-01 0.4333E-01 0.3139E-01 0.2233E-01 0.1550E-01
0.1031E-01 0.6267E-02 0.2957E-02
Output for time t = 0.40000E+00 current h = 0.49754E-01 current order = 3:
0.2055E-02 0.4206E-02 0.6545E-02 0.9167E-02 0.1216E-01 0.1562E-01
0.1964E-01 0.2429E-01 0.2966E-01 0.3582E-01 0.4285E-01 0.5081E-01
0.5976E-01 0.6975E-01 0.8082E-01 0.9300E-01 0.1063E+00 0.1208E+00
0.1363E+00 0.1530E+00 0.1708E+00 0.1897E+00 0.2096E+00 0.2304E+00
0.2521E+00 0.2747E+00 0.2979E+00 0.3219E+00 0.3463E+00 0.3713E+00
0.3967E+00 0.4224E+00 0.4482E+00 0.4743E+00 0.5003E+00 0.5263E+00
0.5522E+00 0.5779E+00 0.6034E+00 0.6284E+00 0.6530E+00 0.6772E+00
0.7008E+00 0.7238E+00 0.7462E+00 0.7679E+00 0.7888E+00 0.8090E+00
0.8282E+00 0.8464E+00 0.8636E+00 0.8796E+00 0.8945E+00 0.9082E+00
0.9206E+00 0.9318E+00 0.9418E+00 0.9506E+00 0.9584E+00 0.9650E+00
0.9707E+00 0.9754E+00 0.9792E+00 0.9822E+00 0.9844E+00 0.9857E+00
0.9861E+00 0.9855E+00 0.9839E+00 0.9809E+00 0.9763E+00 0.9697E+00
0.9608E+00 0.9491E+00 0.9339E+00 0.9146E+00 0.8906E+00 0.8613E+00
0.8262E+00 0.7849E+00 0.7374E+00 0.6841E+00 0.6258E+00 0.5639E+00
0.5000E+00 0.4361E+00 0.3741E+00 0.3156E+00 0.2620E+00 0.2141E+00
0.1724E+00 0.1368E+00 0.1069E+00 0.8219E-01 0.6188E-01 0.4524E-01
0.3147E-01 0.1982E-01 0.9566E-02
Final statistics for mf = 24:
36 steps, 47 res, 13 Jacobians, rwork size = 1309, iwork size = 119
Final output is correct to within 0.4E+00 times local error tolerance
--------------------------------------------------------------------------------
Run with rtol = 0.10E-02 atol = 0.10E-02 mf = 25 npts = 100:
Output for time t = 0.10000E+00 current h = 0.20794E-01 current order = 3:
0.8937E-06 0.2397E-05 0.5502E-05 0.1218E-04 0.2650E-04 0.5674E-04
0.1194E-03 0.2461E-03 0.4957E-03 0.9720E-03 0.1849E-02 0.3399E-02
0.6018E-02 0.1023E-01 0.1670E-01 0.2616E-01 0.3942E-01 0.5730E-01
0.8054E-01 0.1097E+00 0.1451E+00 0.1867E+00 0.2342E+00 0.2871E+00
0.3445E+00 0.4053E+00 0.4681E+00 0.5315E+00 0.5942E+00 0.6550E+00
0.7124E+00 0.7654E+00 0.8131E+00 0.8550E+00 0.8907E+00 0.9202E+00
0.9436E+00 0.9615E+00 0.9745E+00 0.9837E+00 0.9898E+00 0.9938E+00
0.9963E+00 0.9978E+00 0.9988E+00 0.9993E+00 0.9996E+00 0.9998E+00
0.9999E+00 0.9999E+00 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.9999E+00 0.9998E+00 0.9996E+00 0.9992E+00 0.9983E+00 0.9966E+00
0.9935E+00 0.9881E+00 0.9791E+00 0.9648E+00 0.9428E+00 0.9109E+00
0.8663E+00 0.8073E+00 0.7333E+00 0.6462E+00 0.5499E+00 0.4503E+00
0.3540E+00 0.2668E+00 0.1928E+00 0.1337E+00 0.8901E-01 0.5693E-01
0.3500E-01 0.2069E-01 0.1177E-01 0.6463E-02 0.3431E-02 0.1767E-02
0.8858E-03 0.4335E-03 0.2078E-03 0.9780E-04 0.4530E-04 0.2068E-04
0.9287E-05 0.4027E-05 0.1497E-05
Output for time t = 0.20000E+00 current h = 0.28924E-01 current order = 2:
0.1546E-03 0.3436E-03 0.6066E-03 0.9934E-03 0.1569E-02 0.2420E-02
0.3656E-02 0.5415E-02 0.7865E-02 0.1120E-01 0.1563E-01 0.2140E-01
0.2874E-01 0.3789E-01 0.4909E-01 0.6256E-01 0.7848E-01 0.9700E-01
0.1182E+00 0.1422E+00 0.1689E+00 0.1982E+00 0.2300E+00 0.2641E+00
0.3003E+00 0.3381E+00 0.3774E+00 0.4178E+00 0.4588E+00 0.5002E+00
0.5415E+00 0.5823E+00 0.6223E+00 0.6613E+00 0.6988E+00 0.7348E+00
0.7688E+00 0.8008E+00 0.8305E+00 0.8576E+00 0.8821E+00 0.9038E+00
0.9227E+00 0.9388E+00 0.9523E+00 0.9633E+00 0.9722E+00 0.9793E+00
0.9847E+00 0.9889E+00 0.9920E+00 0.9943E+00 0.9960E+00 0.9972E+00
0.9980E+00 0.9986E+00 0.9990E+00 0.9993E+00 0.9994E+00 0.9994E+00
0.9993E+00 0.9990E+00 0.9985E+00 0.9976E+00 0.9961E+00 0.9939E+00
0.9905E+00 0.9856E+00 0.9784E+00 0.9681E+00 0.9538E+00 0.9343E+00
0.9084E+00 0.8749E+00 0.8328E+00 0.7814E+00 0.7210E+00 0.6524E+00
0.5778E+00 0.4999E+00 0.4220E+00 0.3475E+00 0.2790E+00 0.2186E+00
0.1673E+00 0.1251E+00 0.9161E-01 0.6570E-01 0.4620E-01 0.3187E-01
0.2159E-01 0.1436E-01 0.9396E-02 0.6043E-02 0.3819E-02 0.2363E-02
0.1416E-02 0.7900E-03 0.3520E-03
Output for time t = 0.30000E+00 current h = 0.49754E-01 current order = 3:
0.9126E-03 0.1910E-02 0.3079E-02 0.4512E-02 0.6305E-02 0.8562E-02
0.1139E-01 0.1492E-01 0.1925E-01 0.2452E-01 0.3085E-01 0.3836E-01
0.4716E-01 0.5736E-01 0.6904E-01 0.8227E-01 0.9710E-01 0.1136E+00
0.1316E+00 0.1514E+00 0.1726E+00 0.1955E+00 0.2197E+00 0.2454E+00
0.2722E+00 0.3002E+00 0.3292E+00 0.3590E+00 0.3895E+00 0.4205E+00
0.4520E+00 0.4836E+00 0.5154E+00 0.5471E+00 0.5786E+00 0.6097E+00
0.6402E+00 0.6700E+00 0.6991E+00 0.7271E+00 0.7541E+00 0.7799E+00
0.8044E+00 0.8276E+00 0.8492E+00 0.8692E+00 0.8876E+00 0.9043E+00
0.9193E+00 0.9325E+00 0.9441E+00 0.9542E+00 0.9627E+00 0.9700E+00
0.9760E+00 0.9809E+00 0.9850E+00 0.9882E+00 0.9907E+00 0.9926E+00
0.9940E+00 0.9949E+00 0.9953E+00 0.9953E+00 0.9946E+00 0.9933E+00
0.9912E+00 0.9879E+00 0.9833E+00 0.9769E+00 0.9681E+00 0.9563E+00
0.9408E+00 0.9208E+00 0.8954E+00 0.8638E+00 0.8253E+00 0.7796E+00
0.7268E+00 0.6674E+00 0.6027E+00 0.5346E+00 0.4653E+00 0.3972E+00
0.3325E+00 0.2731E+00 0.2202E+00 0.1745E+00 0.1360E+00 0.1044E+00
0.7900E-01 0.5892E-01 0.4333E-01 0.3139E-01 0.2233E-01 0.1550E-01
0.1031E-01 0.6267E-02 0.2957E-02
Output for time t = 0.40000E+00 current h = 0.49754E-01 current order = 3:
0.2055E-02 0.4206E-02 0.6545E-02 0.9167E-02 0.1216E-01 0.1562E-01
0.1964E-01 0.2429E-01 0.2966E-01 0.3582E-01 0.4285E-01 0.5081E-01
0.5976E-01 0.6975E-01 0.8082E-01 0.9300E-01 0.1063E+00 0.1208E+00
0.1363E+00 0.1530E+00 0.1708E+00 0.1897E+00 0.2096E+00 0.2304E+00
0.2521E+00 0.2747E+00 0.2979E+00 0.3219E+00 0.3463E+00 0.3713E+00
0.3967E+00 0.4224E+00 0.4482E+00 0.4743E+00 0.5003E+00 0.5263E+00
0.5522E+00 0.5779E+00 0.6034E+00 0.6284E+00 0.6530E+00 0.6772E+00
0.7008E+00 0.7238E+00 0.7462E+00 0.7679E+00 0.7888E+00 0.8090E+00
0.8282E+00 0.8464E+00 0.8636E+00 0.8796E+00 0.8945E+00 0.9082E+00
0.9206E+00 0.9318E+00 0.9418E+00 0.9506E+00 0.9584E+00 0.9650E+00
0.9707E+00 0.9754E+00 0.9792E+00 0.9822E+00 0.9844E+00 0.9857E+00
0.9861E+00 0.9855E+00 0.9839E+00 0.9809E+00 0.9763E+00 0.9697E+00
0.9608E+00 0.9491E+00 0.9339E+00 0.9146E+00 0.8906E+00 0.8613E+00
0.8262E+00 0.7849E+00 0.7374E+00 0.6841E+00 0.6258E+00 0.5639E+00
0.5000E+00 0.4361E+00 0.3741E+00 0.3156E+00 0.2620E+00 0.2141E+00
0.1724E+00 0.1368E+00 0.1069E+00 0.8219E-01 0.6188E-01 0.4524E-01
0.3147E-01 0.1982E-01 0.9566E-02
Final statistics for mf = 25:
36 steps, 99 res, 13 Jacobians, rwork size = 1309, iwork size = 119
Final output is correct to within 0.4E+00 times local error tolerance
--------------------------------------------------------------------------------
Run with rtol = 0.10E-05 atol = 0.10E-05 mf = 14 npts = 100:
Output for time t = 0.10000E+00 current h = 0.73068E-02 current order = 3:
0.2343E-06 0.8142E-06 0.2455E-05 0.6875E-05 0.1806E-04 0.4468E-04
0.1046E-03 0.2321E-03 0.4899E-03 0.9854E-03 0.1892E-02 0.3476E-02
0.6116E-02 0.1033E-01 0.1675E-01 0.2615E-01 0.3935E-01 0.5718E-01
0.8039E-01 0.1095E+00 0.1449E+00 0.1866E+00 0.2342E+00 0.2871E+00
0.3446E+00 0.4054E+00 0.4682E+00 0.5318E+00 0.5946E+00 0.6554E+00
0.7129E+00 0.7658E+00 0.8134E+00 0.8551E+00 0.8905E+00 0.9196E+00
0.9428E+00 0.9606E+00 0.9738E+00 0.9832E+00 0.9897E+00 0.9939E+00
0.9965E+00 0.9981E+00 0.9990E+00 0.9995E+00 0.9998E+00 0.9999E+00
0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.9999E+00 0.9998E+00 0.9996E+00 0.9992E+00 0.9983E+00 0.9966E+00
0.9935E+00 0.9881E+00 0.9792E+00 0.9648E+00 0.9429E+00 0.9109E+00
0.8663E+00 0.8072E+00 0.7333E+00 0.6462E+00 0.5498E+00 0.4502E+00
0.3538E+00 0.2667E+00 0.1928E+00 0.1337E+00 0.8909E-01 0.5707E-01
0.3516E-01 0.2084E-01 0.1188E-01 0.6510E-02 0.3423E-02 0.1725E-02
0.8322E-03 0.3833E-03 0.1682E-03 0.7012E-04 0.2769E-04 0.1032E-04
0.3609E-05 0.1174E-05 0.3324E-06
Output for time t = 0.20000E+00 current h = 0.63398E-02 current order = 2:
0.1565E-03 0.3492E-03 0.6187E-03 0.1016E-02 0.1605E-02 0.2469E-02
0.3717E-02 0.5481E-02 0.7923E-02 0.1123E-01 0.1563E-01 0.2135E-01
0.2864E-01 0.3776E-01 0.4895E-01 0.6243E-01 0.7838E-01 0.9695E-01
0.1182E+00 0.1422E+00 0.1690E+00 0.1983E+00 0.2301E+00 0.2641E+00
0.3002E+00 0.3380E+00 0.3772E+00 0.4175E+00 0.4586E+00 0.5000E+00
0.5414E+00 0.5825E+00 0.6228E+00 0.6620E+00 0.6998E+00 0.7359E+00
0.7699E+00 0.8017E+00 0.8310E+00 0.8578E+00 0.8818E+00 0.9031E+00
0.9216E+00 0.9376E+00 0.9511E+00 0.9622E+00 0.9714E+00 0.9787E+00
0.9844E+00 0.9888E+00 0.9921E+00 0.9945E+00 0.9963E+00 0.9975E+00
0.9984E+00 0.9989E+00 0.9993E+00 0.9995E+00 0.9996E+00 0.9996E+00
0.9994E+00 0.9991E+00 0.9986E+00 0.9976E+00 0.9962E+00 0.9940E+00
0.9906E+00 0.9856E+00 0.9783E+00 0.9680E+00 0.9537E+00 0.9342E+00
0.9083E+00 0.8748E+00 0.8327E+00 0.7814E+00 0.7210E+00 0.6525E+00
0.5779E+00 0.5000E+00 0.4221E+00 0.3475E+00 0.2790E+00 0.2186E+00
0.1673E+00 0.1252E+00 0.9168E-01 0.6579E-01 0.4630E-01 0.3197E-01
0.2167E-01 0.1442E-01 0.9417E-02 0.6036E-02 0.3791E-02 0.2326E-02
0.1378E-02 0.7604E-03 0.3358E-03
Output for time t = 0.30000E+00 current h = 0.17382E-01 current order = 4:
0.9295E-03 0.1942E-02 0.3124E-02 0.4565E-02 0.6361E-02 0.8616E-02
0.1144E-01 0.1495E-01 0.1926E-01 0.2451E-01 0.3082E-01 0.3831E-01
0.4709E-01 0.5727E-01 0.6894E-01 0.8216E-01 0.9698E-01 0.1134E+00
0.1316E+00 0.1513E+00 0.1726E+00 0.1954E+00 0.2197E+00 0.2454E+00
0.2723E+00 0.3003E+00 0.3293E+00 0.3591E+00 0.3897E+00 0.4208E+00
0.4523E+00 0.4841E+00 0.5159E+00 0.5477E+00 0.5792E+00 0.6103E+00
0.6409E+00 0.6707E+00 0.6997E+00 0.7277E+00 0.7546E+00 0.7803E+00
0.8046E+00 0.8274E+00 0.8487E+00 0.8684E+00 0.8866E+00 0.9030E+00
0.9178E+00 0.9311E+00 0.9427E+00 0.9529E+00 0.9617E+00 0.9691E+00
0.9754E+00 0.9806E+00 0.9849E+00 0.9883E+00 0.9910E+00 0.9930E+00
0.9945E+00 0.9954E+00 0.9958E+00 0.9957E+00 0.9951E+00 0.9937E+00
0.9915E+00 0.9882E+00 0.9835E+00 0.9770E+00 0.9682E+00 0.9564E+00
0.9408E+00 0.9208E+00 0.8953E+00 0.8637E+00 0.8252E+00 0.7795E+00
0.7267E+00 0.6673E+00 0.6027E+00 0.5346E+00 0.4654E+00 0.3973E+00
0.3327E+00 0.2733E+00 0.2205E+00 0.1748E+00 0.1363E+00 0.1046E+00
0.7914E-01 0.5902E-01 0.4339E-01 0.3142E-01 0.2235E-01 0.1550E-01
0.1030E-01 0.6260E-02 0.2953E-02
Output for time t = 0.40000E+00 current h = 0.24310E-01 current order = 4:
0.2051E-02 0.4195E-02 0.6525E-02 0.9134E-02 0.1211E-01 0.1556E-01
0.1955E-01 0.2419E-01 0.2955E-01 0.3571E-01 0.4275E-01 0.5073E-01
0.5972E-01 0.6975E-01 0.8087E-01 0.9309E-01 0.1064E+00 0.1209E+00
0.1365E+00 0.1532E+00 0.1710E+00 0.1898E+00 0.2097E+00 0.2304E+00
0.2520E+00 0.2744E+00 0.2976E+00 0.3214E+00 0.3458E+00 0.3707E+00
0.3961E+00 0.4218E+00 0.4477E+00 0.4738E+00 0.5000E+00 0.5262E+00
0.5523E+00 0.5782E+00 0.6039E+00 0.6293E+00 0.6542E+00 0.6786E+00
0.7024E+00 0.7256E+00 0.7480E+00 0.7696E+00 0.7903E+00 0.8102E+00
0.8290E+00 0.8467E+00 0.8634E+00 0.8790E+00 0.8935E+00 0.9069E+00
0.9191E+00 0.9301E+00 0.9401E+00 0.9490E+00 0.9569E+00 0.9637E+00
0.9696E+00 0.9746E+00 0.9786E+00 0.9818E+00 0.9842E+00 0.9857E+00
0.9862E+00 0.9857E+00 0.9841E+00 0.9811E+00 0.9766E+00 0.9700E+00
0.9612E+00 0.9495E+00 0.9343E+00 0.9151E+00 0.8911E+00 0.8618E+00
0.8265E+00 0.7851E+00 0.7375E+00 0.6841E+00 0.6257E+00 0.5638E+00
0.4999E+00 0.4361E+00 0.3741E+00 0.3157E+00 0.2621E+00 0.2143E+00
0.1726E+00 0.1370E+00 0.1071E+00 0.8239E-01 0.6206E-01 0.4538E-01
0.3158E-01 0.1990E-01 0.9605E-02
Final statistics for mf = 14:
95 steps, 123 res, 20 Jacobians, rwork size = 2002, iwork size = 119
Final output is correct to within 0.6E+00 times local error tolerance
--------------------------------------------------------------------------------
Run with rtol = 0.10E-05 atol = 0.10E-05 mf = 15 npts = 100:
Output for time t = 0.10000E+00 current h = 0.73068E-02 current order = 3:
0.2343E-06 0.8142E-06 0.2455E-05 0.6875E-05 0.1806E-04 0.4468E-04
0.1046E-03 0.2321E-03 0.4899E-03 0.9854E-03 0.1892E-02 0.3476E-02
0.6116E-02 0.1033E-01 0.1675E-01 0.2615E-01 0.3935E-01 0.5718E-01
0.8039E-01 0.1095E+00 0.1449E+00 0.1866E+00 0.2342E+00 0.2871E+00
0.3446E+00 0.4054E+00 0.4682E+00 0.5318E+00 0.5946E+00 0.6554E+00
0.7129E+00 0.7658E+00 0.8134E+00 0.8551E+00 0.8905E+00 0.9196E+00
0.9428E+00 0.9606E+00 0.9738E+00 0.9832E+00 0.9897E+00 0.9939E+00
0.9965E+00 0.9981E+00 0.9990E+00 0.9995E+00 0.9998E+00 0.9999E+00
0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.9999E+00 0.9998E+00 0.9996E+00 0.9992E+00 0.9983E+00 0.9966E+00
0.9935E+00 0.9881E+00 0.9792E+00 0.9648E+00 0.9429E+00 0.9109E+00
0.8663E+00 0.8072E+00 0.7333E+00 0.6462E+00 0.5498E+00 0.4502E+00
0.3538E+00 0.2667E+00 0.1928E+00 0.1337E+00 0.8909E-01 0.5707E-01
0.3516E-01 0.2084E-01 0.1188E-01 0.6510E-02 0.3423E-02 0.1725E-02
0.8322E-03 0.3833E-03 0.1682E-03 0.7012E-04 0.2769E-04 0.1032E-04
0.3609E-05 0.1174E-05 0.3324E-06
Output for time t = 0.20000E+00 current h = 0.63398E-02 current order = 2:
0.1565E-03 0.3492E-03 0.6187E-03 0.1016E-02 0.1605E-02 0.2469E-02
0.3717E-02 0.5481E-02 0.7923E-02 0.1123E-01 0.1563E-01 0.2135E-01
0.2864E-01 0.3776E-01 0.4895E-01 0.6243E-01 0.7838E-01 0.9695E-01
0.1182E+00 0.1422E+00 0.1690E+00 0.1983E+00 0.2301E+00 0.2641E+00
0.3002E+00 0.3380E+00 0.3772E+00 0.4175E+00 0.4586E+00 0.5000E+00
0.5414E+00 0.5825E+00 0.6228E+00 0.6620E+00 0.6998E+00 0.7359E+00
0.7699E+00 0.8017E+00 0.8310E+00 0.8578E+00 0.8818E+00 0.9031E+00
0.9216E+00 0.9376E+00 0.9511E+00 0.9622E+00 0.9714E+00 0.9787E+00
0.9844E+00 0.9888E+00 0.9921E+00 0.9945E+00 0.9963E+00 0.9975E+00
0.9984E+00 0.9989E+00 0.9993E+00 0.9995E+00 0.9996E+00 0.9996E+00
0.9994E+00 0.9991E+00 0.9986E+00 0.9976E+00 0.9962E+00 0.9940E+00
0.9906E+00 0.9856E+00 0.9783E+00 0.9680E+00 0.9537E+00 0.9342E+00
0.9083E+00 0.8748E+00 0.8327E+00 0.7814E+00 0.7210E+00 0.6525E+00
0.5779E+00 0.5000E+00 0.4221E+00 0.3475E+00 0.2790E+00 0.2186E+00
0.1673E+00 0.1252E+00 0.9168E-01 0.6579E-01 0.4630E-01 0.3197E-01
0.2167E-01 0.1442E-01 0.9417E-02 0.6036E-02 0.3791E-02 0.2326E-02
0.1378E-02 0.7604E-03 0.3358E-03
Output for time t = 0.30000E+00 current h = 0.17382E-01 current order = 4:
0.9295E-03 0.1942E-02 0.3124E-02 0.4565E-02 0.6361E-02 0.8616E-02
0.1144E-01 0.1495E-01 0.1926E-01 0.2451E-01 0.3082E-01 0.3831E-01
0.4709E-01 0.5727E-01 0.6894E-01 0.8216E-01 0.9698E-01 0.1134E+00
0.1316E+00 0.1513E+00 0.1726E+00 0.1954E+00 0.2197E+00 0.2454E+00
0.2723E+00 0.3003E+00 0.3293E+00 0.3591E+00 0.3897E+00 0.4208E+00
0.4523E+00 0.4841E+00 0.5159E+00 0.5477E+00 0.5792E+00 0.6103E+00
0.6409E+00 0.6707E+00 0.6997E+00 0.7277E+00 0.7546E+00 0.7803E+00
0.8046E+00 0.8274E+00 0.8487E+00 0.8684E+00 0.8866E+00 0.9030E+00
0.9178E+00 0.9311E+00 0.9427E+00 0.9529E+00 0.9617E+00 0.9691E+00
0.9754E+00 0.9806E+00 0.9849E+00 0.9883E+00 0.9910E+00 0.9930E+00
0.9945E+00 0.9954E+00 0.9958E+00 0.9957E+00 0.9951E+00 0.9937E+00
0.9915E+00 0.9882E+00 0.9835E+00 0.9770E+00 0.9682E+00 0.9564E+00
0.9408E+00 0.9208E+00 0.8953E+00 0.8637E+00 0.8252E+00 0.7795E+00
0.7267E+00 0.6673E+00 0.6027E+00 0.5346E+00 0.4654E+00 0.3973E+00
0.3327E+00 0.2733E+00 0.2205E+00 0.1748E+00 0.1363E+00 0.1046E+00
0.7914E-01 0.5902E-01 0.4339E-01 0.3142E-01 0.2235E-01 0.1550E-01
0.1030E-01 0.6260E-02 0.2953E-02
Output for time t = 0.40000E+00 current h = 0.24310E-01 current order = 4:
0.2051E-02 0.4195E-02 0.6525E-02 0.9134E-02 0.1211E-01 0.1556E-01
0.1955E-01 0.2419E-01 0.2955E-01 0.3571E-01 0.4275E-01 0.5073E-01
0.5972E-01 0.6975E-01 0.8087E-01 0.9309E-01 0.1064E+00 0.1209E+00
0.1365E+00 0.1532E+00 0.1710E+00 0.1898E+00 0.2097E+00 0.2304E+00
0.2520E+00 0.2744E+00 0.2976E+00 0.3214E+00 0.3458E+00 0.3707E+00
0.3961E+00 0.4218E+00 0.4477E+00 0.4738E+00 0.5000E+00 0.5262E+00
0.5523E+00 0.5782E+00 0.6039E+00 0.6293E+00 0.6542E+00 0.6786E+00
0.7024E+00 0.7256E+00 0.7480E+00 0.7696E+00 0.7903E+00 0.8102E+00
0.8290E+00 0.8467E+00 0.8634E+00 0.8790E+00 0.8935E+00 0.9069E+00
0.9191E+00 0.9301E+00 0.9401E+00 0.9490E+00 0.9569E+00 0.9637E+00
0.9696E+00 0.9746E+00 0.9786E+00 0.9818E+00 0.9842E+00 0.9857E+00
0.9862E+00 0.9857E+00 0.9841E+00 0.9811E+00 0.9766E+00 0.9700E+00
0.9612E+00 0.9495E+00 0.9343E+00 0.9151E+00 0.8911E+00 0.8618E+00
0.8265E+00 0.7851E+00 0.7375E+00 0.6841E+00 0.6257E+00 0.5638E+00
0.4999E+00 0.4361E+00 0.3741E+00 0.3157E+00 0.2621E+00 0.2143E+00
0.1726E+00 0.1370E+00 0.1071E+00 0.8239E-01 0.6206E-01 0.4538E-01
0.3158E-01 0.1990E-01 0.9605E-02
Final statistics for mf = 15:
95 steps, 203 res, 20 Jacobians, rwork size = 2002, iwork size = 119
Final output is correct to within 0.6E+00 times local error tolerance
--------------------------------------------------------------------------------
Run with rtol = 0.10E-05 atol = 0.10E-05 mf = 24 npts = 100:
Output for time t = 0.10000E+00 current h = 0.64687E-02 current order = 5:
0.2331E-06 0.8110E-06 0.2449E-05 0.6866E-05 0.1805E-04 0.4468E-04
0.1046E-03 0.2321E-03 0.4900E-03 0.9854E-03 0.1892E-02 0.3476E-02
0.6116E-02 0.1033E-01 0.1675E-01 0.2615E-01 0.3935E-01 0.5718E-01
0.8039E-01 0.1095E+00 0.1449E+00 0.1866E+00 0.2342E+00 0.2871E+00
0.3446E+00 0.4054E+00 0.4682E+00 0.5318E+00 0.5946E+00 0.6554E+00
0.7129E+00 0.7658E+00 0.8134E+00 0.8551E+00 0.8905E+00 0.9196E+00
0.9428E+00 0.9606E+00 0.9738E+00 0.9832E+00 0.9897E+00 0.9939E+00
0.9965E+00 0.9981E+00 0.9990E+00 0.9995E+00 0.9998E+00 0.9999E+00
0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.9999E+00 0.9998E+00 0.9996E+00 0.9992E+00 0.9983E+00 0.9966E+00
0.9935E+00 0.9881E+00 0.9792E+00 0.9648E+00 0.9429E+00 0.9109E+00
0.8663E+00 0.8072E+00 0.7333E+00 0.6462E+00 0.5498E+00 0.4502E+00
0.3538E+00 0.2667E+00 0.1928E+00 0.1337E+00 0.8909E-01 0.5707E-01
0.3516E-01 0.2084E-01 0.1188E-01 0.6510E-02 0.3423E-02 0.1726E-02
0.8323E-03 0.3833E-03 0.1682E-03 0.7010E-04 0.2767E-04 0.1030E-04
0.3600E-05 0.1170E-05 0.3311E-06
Output for time t = 0.20000E+00 current h = 0.11780E-01 current order = 5:
0.1566E-03 0.3492E-03 0.6188E-03 0.1016E-02 0.1605E-02 0.2470E-02
0.3717E-02 0.5481E-02 0.7924E-02 0.1123E-01 0.1563E-01 0.2135E-01
0.2864E-01 0.3776E-01 0.4895E-01 0.6243E-01 0.7838E-01 0.9695E-01
0.1182E+00 0.1422E+00 0.1690E+00 0.1983E+00 0.2301E+00 0.2641E+00
0.3002E+00 0.3380E+00 0.3772E+00 0.4175E+00 0.4586E+00 0.5000E+00
0.5414E+00 0.5825E+00 0.6228E+00 0.6620E+00 0.6998E+00 0.7359E+00
0.7699E+00 0.8017E+00 0.8310E+00 0.8578E+00 0.8818E+00 0.9030E+00
0.9216E+00 0.9376E+00 0.9511E+00 0.9622E+00 0.9714E+00 0.9786E+00
0.9844E+00 0.9888E+00 0.9921E+00 0.9945E+00 0.9963E+00 0.9975E+00
0.9984E+00 0.9989E+00 0.9993E+00 0.9995E+00 0.9996E+00 0.9996E+00
0.9994E+00 0.9991E+00 0.9986E+00 0.9976E+00 0.9962E+00 0.9940E+00
0.9906E+00 0.9856E+00 0.9783E+00 0.9680E+00 0.9537E+00 0.9342E+00
0.9083E+00 0.8748E+00 0.8327E+00 0.7814E+00 0.7210E+00 0.6525E+00
0.5779E+00 0.5000E+00 0.4221E+00 0.3475E+00 0.2790E+00 0.2186E+00
0.1673E+00 0.1252E+00 0.9168E-01 0.6580E-01 0.4630E-01 0.3197E-01
0.2167E-01 0.1442E-01 0.9416E-02 0.6035E-02 0.3791E-02 0.2325E-02
0.1378E-02 0.7601E-03 0.3357E-03
Output for time t = 0.30000E+00 current h = 0.15321E-01 current order = 5:
0.9295E-03 0.1942E-02 0.3124E-02 0.4565E-02 0.6361E-02 0.8616E-02
0.1144E-01 0.1495E-01 0.1926E-01 0.2451E-01 0.3082E-01 0.3831E-01
0.4709E-01 0.5727E-01 0.6894E-01 0.8216E-01 0.9698E-01 0.1134E+00
0.1316E+00 0.1513E+00 0.1726E+00 0.1954E+00 0.2197E+00 0.2454E+00
0.2723E+00 0.3003E+00 0.3293E+00 0.3591E+00 0.3897E+00 0.4208E+00
0.4523E+00 0.4841E+00 0.5159E+00 0.5477E+00 0.5792E+00 0.6103E+00
0.6409E+00 0.6707E+00 0.6997E+00 0.7277E+00 0.7546E+00 0.7803E+00
0.8046E+00 0.8274E+00 0.8487E+00 0.8685E+00 0.8866E+00 0.9030E+00
0.9178E+00 0.9311E+00 0.9427E+00 0.9529E+00 0.9617E+00 0.9691E+00
0.9754E+00 0.9806E+00 0.9849E+00 0.9883E+00 0.9910E+00 0.9930E+00
0.9945E+00 0.9954E+00 0.9958E+00 0.9957E+00 0.9951E+00 0.9937E+00
0.9915E+00 0.9882E+00 0.9835E+00 0.9770E+00 0.9682E+00 0.9564E+00
0.9408E+00 0.9208E+00 0.8953E+00 0.8637E+00 0.8252E+00 0.7795E+00
0.7267E+00 0.6673E+00 0.6027E+00 0.5346E+00 0.4654E+00 0.3973E+00
0.3327E+00 0.2733E+00 0.2205E+00 0.1748E+00 0.1363E+00 0.1046E+00
0.7914E-01 0.5902E-01 0.4339E-01 0.3142E-01 0.2235E-01 0.1550E-01
0.1030E-01 0.6260E-02 0.2953E-02
Output for time t = 0.40000E+00 current h = 0.19409E-01 current order = 5:
0.2051E-02 0.4195E-02 0.6525E-02 0.9134E-02 0.1211E-01 0.1556E-01
0.1955E-01 0.2419E-01 0.2955E-01 0.3571E-01 0.4275E-01 0.5073E-01
0.5972E-01 0.6975E-01 0.8087E-01 0.9309E-01 0.1064E+00 0.1209E+00
0.1365E+00 0.1532E+00 0.1710E+00 0.1898E+00 0.2097E+00 0.2304E+00
0.2520E+00 0.2744E+00 0.2976E+00 0.3214E+00 0.3458E+00 0.3707E+00
0.3961E+00 0.4218E+00 0.4477E+00 0.4738E+00 0.5000E+00 0.5262E+00
0.5523E+00 0.5782E+00 0.6039E+00 0.6292E+00 0.6542E+00 0.6786E+00
0.7024E+00 0.7256E+00 0.7480E+00 0.7696E+00 0.7903E+00 0.8101E+00
0.8290E+00 0.8467E+00 0.8635E+00 0.8790E+00 0.8935E+00 0.9069E+00
0.9191E+00 0.9301E+00 0.9401E+00 0.9490E+00 0.9569E+00 0.9637E+00
0.9696E+00 0.9746E+00 0.9786E+00 0.9818E+00 0.9842E+00 0.9857E+00
0.9862E+00 0.9857E+00 0.9841E+00 0.9811E+00 0.9766E+00 0.9700E+00
0.9612E+00 0.9495E+00 0.9343E+00 0.9151E+00 0.8911E+00 0.8618E+00
0.8265E+00 0.7851E+00 0.7375E+00 0.6841E+00 0.6257E+00 0.5638E+00
0.4999E+00 0.4361E+00 0.3741E+00 0.3157E+00 0.2621E+00 0.2143E+00
0.1726E+00 0.1370E+00 0.1071E+00 0.8239E-01 0.6206E-01 0.4538E-01
0.3158E-01 0.1990E-01 0.9605E-02
Final statistics for mf = 24:
100 steps, 121 res, 18 Jacobians, rwork size = 1309, iwork size = 119
Final output is correct to within 0.7E+00 times local error tolerance
--------------------------------------------------------------------------------
Run with rtol = 0.10E-05 atol = 0.10E-05 mf = 25 npts = 100:
Output for time t = 0.10000E+00 current h = 0.64687E-02 current order = 5:
0.2331E-06 0.8110E-06 0.2449E-05 0.6866E-05 0.1805E-04 0.4468E-04
0.1046E-03 0.2321E-03 0.4900E-03 0.9854E-03 0.1892E-02 0.3476E-02
0.6116E-02 0.1033E-01 0.1675E-01 0.2615E-01 0.3935E-01 0.5718E-01
0.8039E-01 0.1095E+00 0.1449E+00 0.1866E+00 0.2342E+00 0.2871E+00
0.3446E+00 0.4054E+00 0.4682E+00 0.5318E+00 0.5946E+00 0.6554E+00
0.7129E+00 0.7658E+00 0.8134E+00 0.8551E+00 0.8905E+00 0.9196E+00
0.9428E+00 0.9606E+00 0.9738E+00 0.9832E+00 0.9897E+00 0.9939E+00
0.9965E+00 0.9981E+00 0.9990E+00 0.9995E+00 0.9998E+00 0.9999E+00
0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01 0.1000E+01
0.9999E+00 0.9998E+00 0.9996E+00 0.9992E+00 0.9983E+00 0.9966E+00
0.9935E+00 0.9881E+00 0.9792E+00 0.9648E+00 0.9429E+00 0.9109E+00
0.8663E+00 0.8072E+00 0.7333E+00 0.6462E+00 0.5498E+00 0.4502E+00
0.3538E+00 0.2667E+00 0.1928E+00 0.1337E+00 0.8909E-01 0.5707E-01
0.3516E-01 0.2084E-01 0.1188E-01 0.6510E-02 0.3423E-02 0.1726E-02
0.8323E-03 0.3833E-03 0.1682E-03 0.7010E-04 0.2767E-04 0.1030E-04
0.3600E-05 0.1170E-05 0.3311E-06
Output for time t = 0.20000E+00 current h = 0.11780E-01 current order = 5:
0.1566E-03 0.3492E-03 0.6188E-03 0.1016E-02 0.1605E-02 0.2470E-02
0.3717E-02 0.5481E-02 0.7924E-02 0.1123E-01 0.1563E-01 0.2135E-01
0.2864E-01 0.3776E-01 0.4895E-01 0.6243E-01 0.7838E-01 0.9695E-01
0.1182E+00 0.1422E+00 0.1690E+00 0.1983E+00 0.2301E+00 0.2641E+00
0.3002E+00 0.3380E+00 0.3772E+00 0.4175E+00 0.4586E+00 0.5000E+00
0.5414E+00 0.5825E+00 0.6228E+00 0.6620E+00 0.6998E+00 0.7359E+00
0.7699E+00 0.8017E+00 0.8310E+00 0.8578E+00 0.8818E+00 0.9030E+00
0.9216E+00 0.9376E+00 0.9511E+00 0.9622E+00 0.9714E+00 0.9786E+00
0.9844E+00 0.9888E+00 0.9921E+00 0.9945E+00 0.9963E+00 0.9975E+00
0.9984E+00 0.9989E+00 0.9993E+00 0.9995E+00 0.9996E+00 0.9996E+00
0.9994E+00 0.9991E+00 0.9986E+00 0.9976E+00 0.9962E+00 0.9940E+00
0.9906E+00 0.9856E+00 0.9783E+00 0.9680E+00 0.9537E+00 0.9342E+00
0.9083E+00 0.8748E+00 0.8327E+00 0.7814E+00 0.7210E+00 0.6525E+00
0.5779E+00 0.5000E+00 0.4221E+00 0.3475E+00 0.2790E+00 0.2186E+00
0.1673E+00 0.1252E+00 0.9168E-01 0.6580E-01 0.4630E-01 0.3197E-01
0.2167E-01 0.1442E-01 0.9416E-02 0.6035E-02 0.3791E-02 0.2325E-02
0.1378E-02 0.7601E-03 0.3357E-03
Output for time t = 0.30000E+00 current h = 0.15321E-01 current order = 5:
0.9295E-03 0.1942E-02 0.3124E-02 0.4565E-02 0.6361E-02 0.8616E-02
0.1144E-01 0.1495E-01 0.1926E-01 0.2451E-01 0.3082E-01 0.3831E-01
0.4709E-01 0.5727E-01 0.6894E-01 0.8216E-01 0.9698E-01 0.1134E+00
0.1316E+00 0.1513E+00 0.1726E+00 0.1954E+00 0.2197E+00 0.2454E+00
0.2723E+00 0.3003E+00 0.3293E+00 0.3591E+00 0.3897E+00 0.4208E+00
0.4523E+00 0.4841E+00 0.5159E+00 0.5477E+00 0.5792E+00 0.6103E+00
0.6409E+00 0.6707E+00 0.6997E+00 0.7277E+00 0.7546E+00 0.7803E+00
0.8046E+00 0.8274E+00 0.8487E+00 0.8685E+00 0.8866E+00 0.9030E+00
0.9178E+00 0.9311E+00 0.9427E+00 0.9529E+00 0.9617E+00 0.9691E+00
0.9754E+00 0.9806E+00 0.9849E+00 0.9883E+00 0.9910E+00 0.9930E+00
0.9945E+00 0.9954E+00 0.9958E+00 0.9957E+00 0.9951E+00 0.9937E+00
0.9915E+00 0.9882E+00 0.9835E+00 0.9770E+00 0.9682E+00 0.9564E+00
0.9408E+00 0.9208E+00 0.8953E+00 0.8637E+00 0.8252E+00 0.7795E+00
0.7267E+00 0.6673E+00 0.6027E+00 0.5346E+00 0.4654E+00 0.3973E+00
0.3327E+00 0.2733E+00 0.2205E+00 0.1748E+00 0.1363E+00 0.1046E+00
0.7914E-01 0.5902E-01 0.4339E-01 0.3142E-01 0.2235E-01 0.1550E-01
0.1030E-01 0.6260E-02 0.2953E-02
Output for time t = 0.40000E+00 current h = 0.19409E-01 current order = 5:
0.2051E-02 0.4195E-02 0.6525E-02 0.9134E-02 0.1211E-01 0.1556E-01
0.1955E-01 0.2419E-01 0.2955E-01 0.3571E-01 0.4275E-01 0.5073E-01
0.5972E-01 0.6975E-01 0.8087E-01 0.9309E-01 0.1064E+00 0.1209E+00
0.1365E+00 0.1532E+00 0.1710E+00 0.1898E+00 0.2097E+00 0.2304E+00
0.2520E+00 0.2744E+00 0.2976E+00 0.3214E+00 0.3458E+00 0.3707E+00
0.3961E+00 0.4218E+00 0.4477E+00 0.4738E+00 0.5000E+00 0.5262E+00
0.5523E+00 0.5782E+00 0.6039E+00 0.6292E+00 0.6542E+00 0.6786E+00
0.7024E+00 0.7256E+00 0.7480E+00 0.7696E+00 0.7903E+00 0.8101E+00
0.8290E+00 0.8467E+00 0.8635E+00 0.8790E+00 0.8935E+00 0.9069E+00
0.9191E+00 0.9301E+00 0.9401E+00 0.9490E+00 0.9569E+00 0.9637E+00
0.9696E+00 0.9746E+00 0.9786E+00 0.9818E+00 0.9842E+00 0.9857E+00
0.9862E+00 0.9857E+00 0.9841E+00 0.9811E+00 0.9766E+00 0.9700E+00
0.9612E+00 0.9495E+00 0.9343E+00 0.9151E+00 0.8911E+00 0.8618E+00
0.8265E+00 0.7851E+00 0.7375E+00 0.6841E+00 0.6257E+00 0.5638E+00
0.4999E+00 0.4361E+00 0.3741E+00 0.3157E+00 0.2621E+00 0.2143E+00
0.1726E+00 0.1370E+00 0.1071E+00 0.8239E-01 0.6206E-01 0.4538E-01
0.3158E-01 0.1990E-01 0.9605E-02
Final statistics for mf = 25:
100 steps, 193 res, 18 Jacobians, rwork size = 1309, iwork size = 119
Final output is correct to within 0.7E+00 times local error tolerance
********************************************************************************
Run completed. Number of errors encountered = 0
==========Source and Output for LSOIBT Demonstration Program====================
c-----------------------------------------------------------------------
c Demonstration program for the SLSOIBT package.
c This is the version of 12 June 2001.
c
c This version is in single precision.
c
c This program solves a semi-discretized form of the following system
c Of three PDEs (each similar to a Burgers equation):
c
c u(i) = -(u(1)+u(2)+u(3)) u(i) + eta(i) u(i) (i=1,2,3),
c t x xx
c
c on the interval -1 .le. x .le. 1, and with time t .ge. 0.
c The diffusion coefficients are eta(*) = .1, .02, .01.
c The boundary conditions are u(i) = 0 at x = -1 and x = 1 for all i.
c The initial profile for each u(i) is a square wave:
c u(i) = 0 on 1/2 .lt. abs(x) .le. 1
c u(i) = amp(i)/2 on abs(x) = 1/2
c u(i) = amp(i) on 0 .le. abs(x) .lt. 1/2
c where the amplitudes are amp(*) = .2, .3, .5.
c
c A simplified Galerkin treatment of the spatial variable x is used,
c with piecewise linear basis functions on a uniform mesh of 100
c intervals. The result is a system of ODEs in the discrete values
c u(i,k) approximating u(i) (i=1,2,3) at the interior points
c (k = 1,...,99). The ODEs are:
c
c . . .
c (u(i,k-1) + 4 u(i,k) + u(i,k+1))/6 =
c
c -(1/6dx) (c(k-1)dul(i) + 2c(k)(dul(i)+dur(i)) + c(k+1)dur(i))
c
c + (eta(i)/dx**2) (dur(i) - dul(i)) (i=1,2,3, k=1,...,99),
c
c where
c c(j) = u(1,j)+u(2,j)+u(3,j), dx = .02 = the interval size,
c dul(i) = u(i,k) - u(i,k-1), dur(i) = u(i,k+1) - u(i,k).
c Terms involving boundary values (subscripts 0 or 100) are dropped
c from the equations for k = 1 and k = 99 above.
c
c The problem is run for each of the 4 values of mf, and for two values
c of the tolerances. Output is taken at t = .1, .2, .3, .4.
c Output is on unit lout, set to 6 in a data statement below.
c-----------------------------------------------------------------------
external res, addabt, jacbt
integer ncomp, nip, nm1
integer i, io, istate, itol, iwork, jtol, lout, liw, lrw,
1 meth, miter, mf, neq, nerr, nint, nout
real eodsq, r6d
real abermx, atol, dx, errfac, eta, hun, one,
1 rtol, rwork, six, t, tinit, tlast, tout, tols, two, y, ydoti
dimension eta(3), y(297), ydoti(297), tout(4), tols(2)
dimension rwork(7447), iwork(317)
c Pass problem parameters in the common block par.
common /par/ r6d, eodsq(3), ncomp, nip, nm1
c
c Set problem parameters and run parameters
data eta/0.1e0,0.02e0,0.01e0/, tinit/0.0e0/, tlast/0.4e0/
data one/1.0e0/, two/2.0e0/, six/6.0e0/, hun/100.0e0/
data tout/.10e0,.20e0,.30e0,.40e0/
data lout/6/, nout/4/, lrw/7447/, liw/317/
data itol/1/, tols/1.0e-3, 1.0e-6/
c
c Set mesh parameters nint, dxc etc.
nint = 100
ncomp = 3
dx = two/nint
r6d = one/(six*dx)
do 10 i = 1,ncomp
10 eodsq(i) = eta(i)/dx**2
nip = nint - 1
neq = ncomp*nip
nm1 = nip - 1
iwork(1) = ncomp
iwork(2) = nip
c
nerr = 0
c
c Set the initial conditions (for output purposes only).
call setic (nint, ncomp, y)
c
write (lout,1000)
write (lout,1100) (eta(i),i=1,ncomp), tinit, tlast, nint,
1 ncomp, nip, neq
write (lout,1200)
call edit (y, ncomp, nip, lout)
c
c The jtol loop is over error tolerances.
do 200 jtol = 1,2
rtol = tols(jtol)
atol = rtol
c
c The meth/miter loops cover 4 values of method flag mf.
do 100 meth = 1,2
do 100 miter = 1,2
mf = 10*meth + miter
c
c Set the initial conditions.
call setic (nint, ncomp, y)
t = tinit
istate = 0
c
write (lout,1500) rtol, atol, mf
c
c Loop over output times for each case
do 80 io = 1,nout
c
call slsoibt (res, addabt,jacbt, neq, y, ydoti, t, tout(io),
1 itol,rtol,atol, 1, istate, 0, rwork,lrw,iwork,liw, mf)
c
write (lout,2000) t, rwork(11), iwork(14), iwork(11)
if (io .eq. nout) call edit (y, ncomp, nip, lout)
c
c If istate is not 2 on return, print message and go to next case.
if (istate .ne. 2) then
write (lout,4000) mf, t, istate
nerr = nerr + 1
go to 100
endif
c
80 continue
c
c Print final statistics.
write (lout,3000) mf, iwork(11), iwork(12), iwork(13),
1 iwork(17), iwork(18)
c
c Estimate final error and print result.
call maxerr (y, ncomp, nip, abermx)
errfac = abermx/tols(jtol)
if (errfac .lt. hun) then
write (lout,5000) errfac
else
write (lout,5100) errfac
nerr = nerr + 1
endif
100 continue
200 continue
c
write (lout,6000) nerr
stop
c
1000 format(/20x,' Demonstration Problem for SLSOIBT'//
1 10x,'Galerkin method solution of system of 3 PDEs:'//
2 10x,' u(i) = -(u(1)+u(2)+u(3)) u(i) + eta(i) u(i)',
3 5x,'(i=1,2,3)',/16x,'t',27x,'x',16x,'xx'//
4 10x,'x interval is -1 to 1, zero boundary conditions'/
5 10x,'x discretized using piecewise linear basis functions')
1100 format(/10x,'Fixed parameters are as follows:'/
1 13x,'Diffusion coefficients are eta =',3e10.2/
2 13x,'t0 = ',e12.5/13x,'tlast = ',e12.5/
3 13x,'Uniform mesh, number of intervals =',i4/
4 13x,'Block size mb =',i2/13x,'Number of blocks nb =',i4/
5 13x,'ODE system size neq =',i5//)
c
1200 format(/'Initial profiles:'/)
c
1500 format(////90('*')//'Run with rtol =',e9.1,' atol =',e9.1,
1 ' mf =',i3///)
c
2000 format(' At time t =',e12.5,' current h =',e12.5,
1 ' current order =',i2,' current nst =',i5/)
c
3000 format(//'Final statistics for mf = ',i2,':',
1 i5,' steps,',i6,' res,',i6,' jacobians,'/
2 30x, 'rwork size =',i6,', iwork size =',i6)
c
4000 format(//20x,'Final time reached for mf = ',i2,
1 ' was t = ',e12.5/25x,'at which istate = ',i2//)
5000 format('Final output is correct to within ',e9.2,
1 ' times local error tolerance. ')
5100 format('Final output is wrong by ',e9.2,
1 ' times local error tolerance.')
6000 format(//90('*')//'Run completed: ',i3,' errors encountered')
c
c end of main program for the SLSOIBT demonstration problem
end
subroutine setic (nint, mb, y)
c This routine loads the y array with initial data based on a
c square wave profile for each of the mb PDE variables.
c
integer nint, mb, i, k, nip, n14, n34
real y, amp, half, zero
dimension y(mb,*), amp(3)
data zero/0.0e0/, half/0.5e0/, amp/0.2e0,0.3e0,0.5e0/
c
nip = nint - 1
n14 = nint/4
n34 = 3*n14
c
do 15 k = 1,n14-1
do 10 i = 1,mb
10 y(i,k) = zero
15 continue
c
do 20 i = 1,mb
20 y(i,n14) = half*amp(i)
c
do 35 k = n14+1,n34-1
do 30 i = 1,mb
30 y(i,k) = amp(i)
35 continue
c
do 40 i = 1,mb
40 y(i,n34) = half*amp(i)
c
do 55 k = n34+1,nip
do 50 i = 1,mb
50 y(i,k) = zero
55 continue
c
return
c end of subroutine setic
end
subroutine res (n, t, y, v, r, ires)
c This subroutine computes the residual vector
c r = g(t,y) - A(t,y)*v
c using routines gfun and subav.
c If ires = -1, only g(t,y) is returned in r, since A(t,y) does
c not depend on y.
c No changes need to be made to this routine if nip is changed.
c
integer ires, n, ncomp, nip, nm1
real t, y, v, r, r6d, eodsq
dimension y(n), v(n), r(n)
common /par/ r6d, eodsq(3), ncomp, nip, nm1
c
call gfun (t, y, r, ncomp)
if (ires .eq. -1) return
c
call subav (r, v, ncomp)
c
return
c end of subroutine res
end
subroutine gfun (t, y, g, mb)
c This subroutine computes the right-hand side function g(y,t).
c It uses r6d = 1/(6*dx), eodsq(*) = eta(*)/dx**2, nip,
c and nm1 = nip - 1 from the Common block par.
c
integer mb, ncomp, nip, nm1, i, k
real t, y, g, r6d, eodsq, cc, cl, cr, dli, dri, two
dimension g(mb,*), y(mb,*)
common /par/ r6d, eodsq(3), ncomp, nip, nm1
data two/2.0e0/
c
c left-most interior point (k = 1)
cc = y(1,1) + y(2,1) + y(3,1)
cr = y(1,2) + y(2,2) + y(3,2)
do 10 i = 1,mb
dri = y(i,2) - y(i,1)
g(i,1) = -r6d*(two*cc*y(i,2) + cr*dri)
1 + eodsq(i)*(dri - y(i,1))
10 continue
c
c interior points k = 2 to nip-1
do 20 k = 2,nm1
cl = y(1,k-1) + y(2,k-1) + y(3,k-1)
cc = y(1,k) + y(2,k) + y(3,k)
cr = y(1,k+1) + y(2,k+1) + y(3,k+1)
do 15 i = 1,mb
dli = y(i,k) - y(i,k-1)
dri = y(i,k+1) - y(i,k)
g(i,k) = -r6d*(cl*dli + two*cc*(dli + dri) + cr*dri)
1 + eodsq(i)*(dri - dli)
15 continue
20 continue
c
c right-most interior point (k = nip)
cl = y(1,nm1) + y(2,nm1) + y(3,nm1)
cc = y(1,nip) + y(2,nip) + y(3,nip)
do 30 i = 1,mb
dli = y(i,nip) - y(i,nm1)
g(i,nip) = -r6d*(cl*dli - two*cc*y(i,nm1))
1 - eodsq(i)*(y(i,nip) + dli)
30 continue
c
return
c end of subroutine gfun
end
subroutine subav (r, v, mb)
c This routine subtracts the matrix a time the vector v from r,
c in order to form the residual vector, stored in r.
c
integer mb, ncomp, nip, nm1, i, k
real r, v, r6d, eodsq, aa1, aa4, four, one, six
dimension r(mb,*), v(mb,*)
common /par/ r6d, eodsq(3), ncomp, nip, nm1
data one /1.0e0/, four /4.0e0/, six /6.0e0/
c
aa1 = one/six
aa4 = four/six
c
do 10 i = 1,mb
10 r(i,1) = r(i,1) - (aa4*v(i,1) + aa1*v(i,2))
c
do 20 k = 2,nm1
do 15 i = 1,mb
15 r(i,k) = r(i,k) - (aa1*v(i,k-1) + aa4*v(i,k) + aa1*v(i,k+1))
20 continue
c
do 30 i = 1,mb
30 r(i,nip) = r(i,nip) - (aa1*v(i,nm1) + aa4*v(i,nip))
c
return
c end of subroutine subav
end
subroutine addabt (n, t, y, mb, nb, pa, pb, pc)
c This subroutine computes the elements of the matrix A,
c and adds them to pa, pb, and pc in the appropriate manner.
c The matrix A is tridiagonal, of order n, with
c nonzero elements (reading across) of 1/6, 4/6, 1/6.
c
integer n, mb, nb, i, k
real pa, pb, pc, t, y, aa1, aa4, four, one, six
dimension y(mb,nb),pa(mb,mb,nb),pb(mb,mb,nb),pc(mb,mb,nb)
data one/1.0e0/, four/4.0e0/, six/6.0e0/
c
aa1 = one/six
aa4 = four/six
do 50 k = 1,nb
do 10 i = 1,mb
10 pa(i,i,k) = pa(i,i,k) + aa4
if (k .ne. nb) then
do 20 i = 1,mb
20 pb(i,i,k) = pb(i,i,k) + aa1
endif
if (k .ne. 1) then
do 30 i = 1,mb
30 pc(i,i,k) = pc(i,i,k) + aa1
endif
50 continue
c
return
c end of subroutine addabt
end
subroutine jacbt (n, t, y, s, mb, nb, pa, pb, pc)
c This subroutine computes the Jacobian dg/dy = d(g-A*s)/dy
c which has block-tridiagonal structure. The main, upper, and
c lower diagonals are stored in pa, pb, and pc, respectively.
c
integer n, mb, nb, ncomp, nip, nm1, i, j, k
real t, y, s, pa, pb, pc, r6d, eodsq, cc, cl, cr,
1 dlj, drj, paij, pbij, pcij, terma, termb, termc, two
dimension y(mb,nb),s(n),pa(mb,mb,nb),pb(mb,mb,nb),pc(mb,mb,nb)
common /par/ r6d, eodsq(3), ncomp, nip, nm1
data two/2.0e0/
c
c left-most interior point (k = 1)
cc = y(1,1) + y(2,1) + y(3,1)
cr = y(1,2) + y(2,2) + y(3,2)
terma = r6d*cr
termb = -r6d*(two*cc + cr)
do 20 j = 1,mb
drj = y(j,2) - y(j,1)
paij = -r6d*two*y(j,2)
pbij = -r6d*drj
do 10 i = 1,mb
pa(i,j,1) = paij
10 pb(i,j,1) = pbij
pa(j,j,1) = pa(j,j,1) + terma - two*eodsq(j)
pb(j,j,1) = pb(j,j,1) + termb + eodsq(j)
20 continue
c
c interior points k = 2 to nip-1
do 50 k = 2,nm1
cl = y(1,k-1) + y(2,k-1) + y(3,k-1)
cc = y(1,k) + y(2,k) + y(3,k)
cr = y(1,k+1) + y(2,k+1) + y(3,k+1)
terma = r6d*(cr - cl)
termb = -r6d*(two*cc + cr)
termc = r6d*(two*cc + cl)
do 40 j = 1,mb
dlj = y(j,k) - y(j,k-1)
drj = y(j,k+1) - y(j,k)
paij = -r6d*two*(dlj + drj)
pbij = -r6d*drj
pcij = -r6d*dlj
do 30 i = 1,mb
pa(i,j,k) = paij
pb(i,j,k) = pbij
30 pc(i,j,k) = pcij
pa(j,j,k) = pa(j,j,k) + terma - two*eodsq(j)
pb(j,j,k) = pb(j,j,k) + termb + eodsq(j)
pc(j,j,k) = pc(j,j,k) + termc + eodsq(j)
40 continue
50 continue
c
c right-most interior point (k = nip)
cl = y(1,nm1) + y(2,nm1) + y(3,nm1)
cc = y(1,nip) + y(2,nip) + y(3,nip)
terma = -r6d*cl
termc = r6d*(two*cc + cl)
do 70 j = 1,mb
dlj = y(j,nip) - y(j,nm1)
paij = r6d*two*y(j,nm1)
pcij = -r6d*dlj
do 60 i = 1,mb
pa(i,j,nip) = paij
60 pc(i,j,nip) = pcij
pa(j,j,nip) = pa(j,j,nip) + terma - two*eodsq(j)
pc(j,j,nip) = pc(j,j,nip) + termc + eodsq(j)
70 continue
c
return
c end of subroutine jacbt
end
subroutine edit (y, mb, nip, lout)
c This routine prints output. For each of the mb PDE components, the
c values at the nip points are printed. All output is on unit lout.
c
integer mb, nip, lout, i, k
real y
dimension y(mb,nip)
c
do 10 i = 1,mb
10 write (lout,20) i, (y(i,k),k=1,nip)
c
20 format(' Values of PDE component i =',i3/15(7e12.4/))
c
return
c end of subroutine edit
end
subroutine maxerr (y, mb, nb, abermx)
c This routine computes the maximum absolute error in the y array,
c as a computed solution at t = 0.4, using data-loaded values for
c accurate answers (from running with much smaller tolerances).
c
integer mb, nb, k
real y, abermx, ae1, ae2, ae3, u1, u2, u3, zero,
1 u1a, u1b, u1c, u1d, u1e, u1f, u1g,
2 u2a, u2b, u2c, u2d, u2e, u2f, u2g,
3 u3a, u3b, u3c, u3d, u3e, u3f, u3g
dimension y(mb,nb), u1(99), u2(99), u3(99)
dimension u1a(16),u1b(16),u1c(16),u1d(16),u1e(16),u1f(16),u1g(3),
2 u2a(16),u2b(16),u2c(16),u2d(16),u2e(16),u2f(16),u2g(3),
3 u3a(16),u3b(16),u3c(16),u3d(16),u3e(16),u3f(16),u3g(3)
equivalence (u1a(1),u1(1)), (u1b(1),u1(17)),
1 (u1c(1),u1(33)), (u1d(1),u1(49)), (u1e(1),u1(65)),
1 (u1f(1),u1(81)), (u1g(1),u1(97))
equivalence (u2a(1),u2(1)), (u2b(1),u2(17)),
1 (u2c(1),u2(33)), (u2d(1),u2(49)), (u2e(1),u2(65)),
1 (u2f(1),u2(81)), (u2g(1),u2(97))
equivalence (u3a(1),u3(1)), (u3b(1),u3(17)),
1 (u3c(1),u3(33)), (u3d(1),u3(49)), (u3e(1),u3(65)),
1 (u3f(1),u3(81)), (u3g(1),u3(97))
c
data u1a /
1 1.70956682e-03, 3.43398445e-03, 5.18783349e-03, 6.98515842e-03,
1 8.83921016e-03, 1.07622016e-02, 1.27650806e-02, 1.48573251e-02,
1 1.70467655e-02, 1.93394396e-02, 2.17394852e-02, 2.42490773e-02,
1 2.68684152e-02, 2.95957660e-02, 3.24275691e-02, 3.53586054e-02/
data u1b /
1 3.83822285e-02, 4.14906520e-02, 4.46752791e-02, 4.79270545e-02,
1 5.12368132e-02, 5.45956048e-02, 5.79949684e-02, 6.14271460e-02,
1 6.48852271e-02, 6.83632267e-02, 7.18561029e-02, 7.53597274e-02,
1 7.88708192e-02, 8.23868545e-02, 8.59059616e-02, 8.94268082e-02/
data u1c /
1 9.29484864e-02, 9.64703968e-02, 9.99921344e-02, 1.03513375e-01,
1 1.07033760e-01, 1.10552783e-01, 1.14069668e-01, 1.17583246e-01,
1 1.21091827e-01, 1.24593066e-01, 1.28083828e-01, 1.31560049e-01,
1 1.35016617e-01, 1.38447256e-01, 1.41844451e-01, 1.45199401e-01/
data u1d /
1 1.48502033e-01, 1.51741065e-01, 1.54904135e-01, 1.57977973e-01,
1 1.60948623e-01, 1.63801670e-01, 1.66522463e-01, 1.69096305e-01,
1 1.71508595e-01, 1.73744902e-01, 1.75790974e-01, 1.77632682e-01,
1 1.79255895e-01, 1.80646319e-01, 1.81789276e-01, 1.82669470e-01/
data u1e /
1 1.83270725e-01, 1.83575716e-01, 1.83565712e-01, 1.83220322e-01,
1 1.82517279e-01, 1.81432251e-01, 1.79938706e-01, 1.78007835e-01,
1 1.75608540e-01, 1.72707519e-01, 1.69269456e-01, 1.65257378e-01,
1 1.60633244e-01, 1.55358941e-01, 1.49398029e-01, 1.42718981e-01/
data u1f /
1 1.35301474e-01, 1.27148627e-01, 1.18308730e-01, 1.08905085e-01,
1 9.91559295e-02, 8.93515884e-02, 7.97824293e-02, 7.06663514e-02,
1 6.21244732e-02, 5.41994827e-02, 4.68848207e-02, 4.01465202e-02,
1 3.39357642e-02, 2.81954415e-02, 2.28635569e-02, 1.78750916e-02/
data u1g / 1.31630892e-02, 8.65933391e-03, 4.29480447e-03/
data u2a /
1 7.17416019e-06, 1.70782645e-05, 3.31245126e-05, 6.01588363e-05,
1 1.05339286e-04, 1.79174771e-04, 2.96719122e-04, 4.78862606e-04,
1 7.53598916e-04, 1.15707860e-03, 1.73420412e-03, 2.53849668e-03,
1 3.63099110e-03, 5.07800919e-03, 6.94782549e-03, 9.30645443e-03/
data u2b /
1 1.22130079e-02, 1.57152366e-02, 1.98459102e-02, 2.46205841e-02,
1 3.00370492e-02, 3.60764461e-02, 4.27057301e-02, 4.98809820e-02,
1 5.75510102e-02, 6.56607602e-02, 7.41541974e-02, 8.29764928e-02,
1 9.20754824e-02, 1.01402468e-01, 1.10912474e-01, 1.20564094e-01/
data u2c /
1 1.30319039e-01, 1.40141489e-01, 1.49997326e-01, 1.59853293e-01,
1 1.69676126e-01, 1.79431680e-01, 1.89084097e-01, 1.98595037e-01,
1 2.07923034e-01, 2.17023055e-01, 2.25846345e-01, 2.34340694e-01,
1 2.42451240e-01, 2.50121934e-01, 2.57297724e-01, 2.63927433e-01/
data u2d /
1 2.69967170e-01, 2.75383917e-01, 2.80158840e-01, 2.84289739e-01,
1 2.87792167e-01, 2.90698875e-01, 2.93057586e-01, 2.94927384e-01,
1 2.96374262e-01, 2.97466488e-01, 2.98270390e-01, 2.98847025e-01,
1 2.99249945e-01, 2.99524080e-01, 2.99705593e-01, 2.99822450e-01/
data u2e /
1 2.99895431e-01, 2.99939301e-01, 2.99963931e-01, 2.99975129e-01,
1 2.99974996e-01, 2.99961526e-01, 2.99927041e-01, 2.99854809e-01,
1 2.99712769e-01, 2.99442742e-01, 2.98942676e-01, 2.98038511e-01,
1 2.96441259e-01, 2.93684573e-01, 2.89040478e-01, 2.81421884e-01/
data u2f /
1 2.69315148e-01, 2.50874185e-01, 2.24457680e-01, 1.89885662e-01,
1 1.49894358e-01, 1.09927672e-01, 7.54041273e-02, 4.90259517e-02,
1 3.06080023e-02, 1.85165524e-02, 1.09104125e-02, 6.27726960e-03,
1 3.53002680e-03, 1.94049735e-03, 1.04218859e-03, 5.45964314e-04/
data u2g / 2.77379128e-04, 1.33343739e-04, 5.32660444e-05/
data u3a /
1 1.86765383e-10, 1.96772458e-09, 1.19111389e-08, 5.54964761e-08,
1 2.18340713e-07, 7.55899524e-07, 2.35604385e-06, 6.70801745e-06,
1 1.76224112e-05, 4.30351929e-05, 9.82592148e-05, 2.10736217e-04,
1 4.26209304e-04, 8.15657041e-04, 1.48160943e-03, 2.56186555e-03/
data u3b /
1 4.22851247e-03, 6.68078970e-03, 1.01317466e-02, 1.47903961e-02,
1 2.08424987e-02, 2.84336008e-02, 3.76573037e-02, 4.85502549e-02,
1 6.10936693e-02, 7.52198901e-02, 9.08218891e-02, 1.07763660e-01,
1 1.25889931e-01, 1.45034247e-01, 1.65025016e-01, 1.85689556e-01/
data u3c /
1 2.06856371e-01, 2.28356037e-01, 2.50021072e-01, 2.71685149e-01,
1 2.93181998e-01, 3.14344301e-01, 3.35002907e-01, 3.54986687e-01,
1 3.74123404e-01, 3.92241969e-01, 4.09176451e-01, 4.24772089e-01,
1 4.38893320e-01, 4.51433444e-01, 4.62324969e-01, 4.71549073e-01/
data u3d /
1 4.79142163e-01, 4.85197409e-01, 4.89859810e-01, 4.93314543e-01,
1 4.95770115e-01, 4.97439231e-01, 4.98520996e-01, 4.99187563e-01,
1 4.99576941e-01, 4.99791928e-01, 4.99903753e-01, 4.99958343e-01,
1 4.99983239e-01, 4.99993785e-01, 4.99997902e-01, 4.99999367e-01/
data u3e /
1 4.99999835e-01, 4.99999965e-01, 4.99999995e-01, 5.00000000e-01,
1 5.00000000e-01, 4.99999997e-01, 4.99999976e-01, 4.99999863e-01,
1 4.99999315e-01, 4.99996914e-01, 4.99987300e-01, 4.99951740e-01,
1 4.99829328e-01, 4.99435130e-01, 4.98245007e-01, 4.94883400e-01/
data u3f /
1 4.86081966e-01, 4.65174923e-01, 4.21856650e-01, 3.47885738e-01,
1 2.49649938e-01, 1.51648615e-01, 7.80173239e-02, 3.47983164e-02,
1 1.38686441e-02, 5.05765688e-03, 1.71052539e-03, 5.38966324e-04,
1 1.57923694e-04, 4.27352191e-05, 1.05512005e-05, 2.33068621e-06/
data u3g / 4.45404604e-07, 6.88336884e-08, 7.23875975e-09/
data zero/0.0e0/
c
abermx = zero
do 10 k = 1,99
ae1 = abs(y(1,k) - u1(k))
ae2 = abs(y(2,k) - u2(k))
ae3 = abs(y(3,k) - u3(k))
abermx = max(abermx, ae1, ae2, ae3)
10 continue
c
return
c end of subroutine maxerr
end
................................................................................
Demonstration Problem for DLSOIBT
Galerkin method solution of system of 3 PDEs:
u(i) = -(u(1)+u(2)+u(3)) u(i) + eta(i) u(i) (i=1,2,3)
t x xx
x interval is -1 to 1, zero boundary conditions
x discretized using piecewise linear basis functions
Fixed parameters are as follows:
Diffusion coefficients are eta = 0.10E+00 0.20E-01 0.10E-01
t0 = 0.00000E+00
tlast = 0.40000E+00
Uniform mesh, number of intervals = 100
Block size mb = 3
Number of blocks nb = 99
ODE system size neq = 297
Initial profiles:
Values of PDE component i = 1
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.1000E+00 0.2000E+00 0.2000E+00 0.2000E+00
0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00
0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00
0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00
0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00
0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00
0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00
0.2000E+00 0.2000E+00 0.2000E+00 0.2000E+00 0.1000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00
Values of PDE component i = 2
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.1500E+00 0.3000E+00 0.3000E+00 0.3000E+00
0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00
0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00
0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00
0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00
0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00
0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00
0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00 0.1500E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00
Values of PDE component i = 3
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.2500E+00 0.5000E+00 0.5000E+00 0.5000E+00
0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00
0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00
0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00
0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00
0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00
0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00
0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.2500E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00
0.0000E+00
******************************************************************************************
Run with rtol = 0.1E-02 atol = 0.1E-02 mf = 11
At time t = 0.10000E+00 current h = 0.22309E-01 current order = 2 current nst = 17
At time t = 0.20000E+00 current h = 0.41111E-01 current order = 2 current nst = 20
At time t = 0.30000E+00 current h = 0.51073E-01 current order = 2 current nst = 22
At time t = 0.40000E+00 current h = 0.58735E-01 current order = 2 current nst = 24
Values of PDE component i = 1
0.1714E-02 0.3444E-02 0.5203E-02 0.7006E-02 0.8866E-02 0.1079E-01 0.1280E-01
0.1490E-01 0.1710E-01 0.1940E-01 0.2181E-01 0.2433E-01 0.2695E-01 0.2968E-01
0.3252E-01 0.3546E-01 0.3848E-01 0.4161E-01 0.4476E-01 0.4807E-01 0.5130E-01
0.5475E-01 0.5807E-01 0.6152E-01 0.6497E-01 0.6846E-01 0.7191E-01 0.7531E-01
0.7899E-01 0.8240E-01 0.8592E-01 0.8937E-01 0.9290E-01 0.9639E-01 0.9989E-01
0.1034E+00 0.1069E+00 0.1104E+00 0.1139E+00 0.1174E+00 0.1209E+00 0.1244E+00
0.1279E+00 0.1313E+00 0.1348E+00 0.1383E+00 0.1417E+00 0.1451E+00 0.1484E+00
0.1517E+00 0.1549E+00 0.1580E+00 0.1610E+00 0.1639E+00 0.1666E+00 0.1692E+00
0.1717E+00 0.1739E+00 0.1760E+00 0.1778E+00 0.1794E+00 0.1808E+00 0.1819E+00
0.1828E+00 0.1834E+00 0.1836E+00 0.1836E+00 0.1832E+00 0.1825E+00 0.1814E+00
0.1799E+00 0.1779E+00 0.1755E+00 0.1725E+00 0.1691E+00 0.1650E+00 0.1603E+00
0.1548E+00 0.1488E+00 0.1424E+00 0.1348E+00 0.1266E+00 0.1176E+00 0.1082E+00
0.9850E-01 0.8871E-01 0.7919E-01 0.7011E-01 0.6161E-01 0.5373E-01 0.4646E-01
0.3977E-01 0.3361E-01 0.2792E-01 0.2263E-01 0.1770E-01 0.1303E-01 0.8572E-02
0.4251E-02
Values of PDE component i = 2
0.7744E-05 0.1814E-04 0.3450E-04 0.6154E-04 0.1063E-03 0.1791E-03 0.2948E-03
0.4744E-03 0.7460E-03 0.1146E-02 0.1721E-02 0.2524E-02 0.3617E-02 0.5068E-02
0.6946E-02 0.9315E-02 0.1223E-01 0.1575E-01 0.1989E-01 0.2467E-01 0.3009E-01
0.3613E-01 0.4275E-01 0.4991E-01 0.5755E-01 0.6565E-01 0.7409E-01 0.8288E-01
0.9193E-01 0.1012E+00 0.1106E+00 0.1202E+00 0.1299E+00 0.1396E+00 0.1494E+00
0.1592E+00 0.1690E+00 0.1787E+00 0.1885E+00 0.1981E+00 0.2076E+00 0.2170E+00
0.2260E+00 0.2348E+00 0.2431E+00 0.2510E+00 0.2582E+00 0.2649E+00 0.2709E+00
0.2762E+00 0.2808E+00 0.2847E+00 0.2880E+00 0.2907E+00 0.2929E+00 0.2946E+00
0.2960E+00 0.2970E+00 0.2978E+00 0.2984E+00 0.2989E+00 0.2992E+00 0.2994E+00
0.2996E+00 0.2997E+00 0.2998E+00 0.2999E+00 0.2999E+00 0.2999E+00 0.2999E+00
0.2999E+00 0.2998E+00 0.2997E+00 0.2995E+00 0.2990E+00 0.2983E+00 0.2967E+00
0.2937E+00 0.2890E+00 0.2817E+00 0.2700E+00 0.2505E+00 0.2224E+00 0.1867E+00
0.1467E+00 0.1076E+00 0.7410E-01 0.4856E-01 0.3063E-01 0.1876E-01 0.1121E-01
0.6560E-02 0.3762E-02 0.2117E-02 0.1169E-02 0.6331E-03 0.3338E-03 0.1667E-03
0.6863E-04
Values of PDE component i = 3
0.9946E-07 0.2111E-06 0.3530E-06 0.5634E-06 0.9413E-06 0.1748E-05 0.3651E-05
0.8255E-05 0.1918E-04 0.4406E-04 0.9777E-04 0.2074E-03 0.4186E-03 0.8031E-03
0.1465E-02 0.2544E-02 0.4215E-02 0.6676E-02 0.1014E-01 0.1480E-01 0.2085E-01
0.2842E-01 0.3759E-01 0.4839E-01 0.6081E-01 0.7478E-01 0.9019E-01 0.1069E+00
0.1248E+00 0.1437E+00 0.1634E+00 0.1839E+00 0.2049E+00 0.2264E+00 0.2481E+00
0.2701E+00 0.2921E+00 0.3140E+00 0.3356E+00 0.3565E+00 0.3766E+00 0.3955E+00
0.4129E+00 0.4286E+00 0.4425E+00 0.4545E+00 0.4646E+00 0.4730E+00 0.4798E+00
0.4851E+00 0.4892E+00 0.4923E+00 0.4946E+00 0.4962E+00 0.4974E+00 0.4983E+00
0.4988E+00 0.4992E+00 0.4995E+00 0.4997E+00 0.4998E+00 0.4999E+00 0.4999E+00
0.4999E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00
0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5001E+00 0.5002E+00
0.4993E+00 0.4986E+00 0.4997E+00 0.4870E+00 0.4577E+00 0.4177E+00 0.3451E+00
0.2443E+00 0.1485E+00 0.7868E-01 0.3717E-01 0.1608E-01 0.6517E-02 0.2512E-02
0.9293E-03 0.3318E-03 0.1145E-03 0.3809E-04 0.1208E-04 0.3554E-05 0.9159E-06
0.1828E-06
Final statistics for mf = 11: 24 steps, 38 res, 9 jacobians,
rwork size = 7447, iwork size = 317
Final output is correct to within 0.75E+01 times local error tolerance.
******************************************************************************************
Run with rtol = 0.1E-02 atol = 0.1E-02 mf = 12
At time t = 0.10000E+00 current h = 0.22305E-01 current order = 2 current nst = 17
At time t = 0.20000E+00 current h = 0.41173E-01 current order = 2 current nst = 20
At time t = 0.30000E+00 current h = 0.51349E-01 current order = 2 current nst = 22
At time t = 0.40000E+00 current h = 0.59258E-01 current order = 2 current nst = 24
Values of PDE component i = 1
0.1712E-02 0.3440E-02 0.5197E-02 0.6997E-02 0.8855E-02 0.1078E-01 0.1279E-01
0.1488E-01 0.1708E-01 0.1937E-01 0.2178E-01 0.2429E-01 0.2691E-01 0.2963E-01
0.3247E-01 0.3540E-01 0.3841E-01 0.4153E-01 0.4468E-01 0.4797E-01 0.5119E-01
0.5464E-01 0.5793E-01 0.6141E-01 0.6483E-01 0.6828E-01 0.7182E-01 0.7520E-01
0.7881E-01 0.8223E-01 0.8579E-01 0.8925E-01 0.9278E-01 0.9628E-01 0.9978E-01
0.1033E+00 0.1068E+00 0.1103E+00 0.1138E+00 0.1173E+00 0.1208E+00 0.1243E+00
0.1278E+00 0.1313E+00 0.1348E+00 0.1383E+00 0.1417E+00 0.1451E+00 0.1485E+00
0.1517E+00 0.1549E+00 0.1580E+00 0.1611E+00 0.1639E+00 0.1667E+00 0.1693E+00
0.1717E+00 0.1739E+00 0.1760E+00 0.1778E+00 0.1794E+00 0.1808E+00 0.1819E+00
0.1828E+00 0.1834E+00 0.1837E+00 0.1836E+00 0.1833E+00 0.1826E+00 0.1814E+00
0.1800E+00 0.1779E+00 0.1756E+00 0.1726E+00 0.1692E+00 0.1652E+00 0.1605E+00
0.1553E+00 0.1493E+00 0.1427E+00 0.1352E+00 0.1271E+00 0.1182E+00 0.1088E+00
0.9905E-01 0.8926E-01 0.7972E-01 0.7062E-01 0.6210E-01 0.5418E-01 0.4687E-01
0.4013E-01 0.3392E-01 0.2818E-01 0.2285E-01 0.1786E-01 0.1315E-01 0.8653E-02
0.4292E-02
Values of PDE component i = 2
0.7637E-05 0.1793E-04 0.3419E-04 0.6115E-04 0.1058E-03 0.1786E-03 0.2943E-03
0.4739E-03 0.7456E-03 0.1146E-02 0.1720E-02 0.2523E-02 0.3617E-02 0.5068E-02
0.6944E-02 0.9312E-02 0.1223E-01 0.1574E-01 0.1988E-01 0.2465E-01 0.3006E-01
0.3608E-01 0.4269E-01 0.4983E-01 0.5745E-01 0.6552E-01 0.7394E-01 0.8271E-01
0.9173E-01 0.1010E+00 0.1104E+00 0.1200E+00 0.1297E+00 0.1395E+00 0.1493E+00
0.1591E+00 0.1690E+00 0.1788E+00 0.1885E+00 0.1982E+00 0.2077E+00 0.2171E+00
0.2261E+00 0.2349E+00 0.2432E+00 0.2510E+00 0.2583E+00 0.2650E+00 0.2710E+00
0.2763E+00 0.2808E+00 0.2848E+00 0.2880E+00 0.2907E+00 0.2929E+00 0.2946E+00
0.2960E+00 0.2970E+00 0.2978E+00 0.2984E+00 0.2989E+00 0.2992E+00 0.2994E+00
0.2996E+00 0.2997E+00 0.2998E+00 0.2999E+00 0.2999E+00 0.2999E+00 0.2999E+00
0.2999E+00 0.2998E+00 0.2997E+00 0.2995E+00 0.2990E+00 0.2982E+00 0.2967E+00
0.2939E+00 0.2892E+00 0.2818E+00 0.2698E+00 0.2505E+00 0.2233E+00 0.1883E+00
0.1484E+00 0.1090E+00 0.7518E-01 0.4929E-01 0.3109E-01 0.1904E-01 0.1137E-01
0.6649E-02 0.3811E-02 0.2144E-02 0.1184E-02 0.6409E-03 0.3380E-03 0.1688E-03
0.6954E-04
Values of PDE component i = 3
0.4971E-08 0.1654E-07 0.4938E-07 0.1430E-06 0.4036E-06 0.1108E-05 0.2946E-05
0.7554E-05 0.1859E-04 0.4372E-04 0.9783E-04 0.2080E-03 0.4199E-03 0.8052E-03
0.1468E-02 0.2548E-02 0.4220E-02 0.6682E-02 0.1015E-01 0.1482E-01 0.2087E-01
0.2845E-01 0.3764E-01 0.4847E-01 0.6093E-01 0.7494E-01 0.9039E-01 0.1072E+00
0.1251E+00 0.1440E+00 0.1638E+00 0.1843E+00 0.2053E+00 0.2268E+00 0.2485E+00
0.2704E+00 0.2924E+00 0.3143E+00 0.3358E+00 0.3567E+00 0.3768E+00 0.3956E+00
0.4130E+00 0.4287E+00 0.4426E+00 0.4546E+00 0.4647E+00 0.4731E+00 0.4798E+00
0.4851E+00 0.4892E+00 0.4923E+00 0.4946E+00 0.4963E+00 0.4974E+00 0.4983E+00
0.4988E+00 0.4992E+00 0.4995E+00 0.4997E+00 0.4998E+00 0.4999E+00 0.4999E+00
0.4999E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00
0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5001E+00 0.5002E+00
0.4993E+00 0.4985E+00 0.4997E+00 0.4872E+00 0.4581E+00 0.4191E+00 0.3472E+00
0.2462E+00 0.1500E+00 0.7966E-01 0.3769E-01 0.1632E-01 0.6615E-02 0.2551E-02
0.9450E-03 0.3386E-03 0.1179E-03 0.4004E-04 0.1329E-04 0.4317E-05 0.1366E-05
0.3917E-06
Final statistics for mf = 12: 24 steps, 128 res, 9 jacobians,
rwork size = 7447, iwork size = 317
Final output is correct to within 0.71E+01 times local error tolerance.
******************************************************************************************
Run with rtol = 0.1E-02 atol = 0.1E-02 mf = 21
At time t = 0.10000E+00 current h = 0.17227E-01 current order = 2 current nst = 20
At time t = 0.20000E+00 current h = 0.33122E-01 current order = 2 current nst = 24
At time t = 0.30000E+00 current h = 0.33122E-01 current order = 2 current nst = 27
At time t = 0.40000E+00 current h = 0.33122E-01 current order = 2 current nst = 30
Values of PDE component i = 1
0.1714E-02 0.3443E-02 0.5202E-02 0.7005E-02 0.8866E-02 0.1080E-01 0.1281E-01
0.1491E-01 0.1711E-01 0.1942E-01 0.2183E-01 0.2435E-01 0.2698E-01 0.2971E-01
0.3255E-01 0.3549E-01 0.3851E-01 0.4162E-01 0.4480E-01 0.4804E-01 0.5134E-01
0.5468E-01 0.5807E-01 0.6148E-01 0.6492E-01 0.6838E-01 0.7185E-01 0.7533E-01
0.7882E-01 0.8230E-01 0.8579E-01 0.8928E-01 0.9277E-01 0.9626E-01 0.9975E-01
0.1032E+00 0.1067E+00 0.1102E+00 0.1137E+00 0.1173E+00 0.1208E+00 0.1243E+00
0.1278E+00 0.1314E+00 0.1349E+00 0.1384E+00 0.1419E+00 0.1453E+00 0.1487E+00
0.1520E+00 0.1552E+00 0.1583E+00 0.1613E+00 0.1642E+00 0.1670E+00 0.1696E+00
0.1720E+00 0.1742E+00 0.1762E+00 0.1780E+00 0.1796E+00 0.1809E+00 0.1820E+00
0.1829E+00 0.1834E+00 0.1837E+00 0.1836E+00 0.1832E+00 0.1825E+00 0.1813E+00
0.1798E+00 0.1779E+00 0.1755E+00 0.1726E+00 0.1692E+00 0.1652E+00 0.1606E+00
0.1553E+00 0.1493E+00 0.1426E+00 0.1351E+00 0.1269E+00 0.1180E+00 0.1085E+00
0.9878E-01 0.8900E-01 0.7947E-01 0.7039E-01 0.6188E-01 0.5397E-01 0.4668E-01
0.3996E-01 0.3376E-01 0.2804E-01 0.2273E-01 0.1777E-01 0.1308E-01 0.8605E-02
0.4268E-02
Values of PDE component i = 2
0.8292E-05 0.1926E-04 0.3621E-04 0.6381E-04 0.1089E-03 0.1817E-03 0.2968E-03
0.4749E-03 0.7439E-03 0.1141E-02 0.1711E-02 0.2511E-02 0.3603E-02 0.5056E-02
0.6939E-02 0.9318E-02 0.1225E-01 0.1578E-01 0.1993E-01 0.2471E-01 0.3012E-01
0.3614E-01 0.4273E-01 0.4984E-01 0.5743E-01 0.6546E-01 0.7385E-01 0.8257E-01
0.9156E-01 0.1008E+00 0.1102E+00 0.1197E+00 0.1294E+00 0.1392E+00 0.1491E+00
0.1591E+00 0.1691E+00 0.1791E+00 0.1891E+00 0.1990E+00 0.2088E+00 0.2183E+00
0.2274E+00 0.2362E+00 0.2444E+00 0.2520E+00 0.2591E+00 0.2655E+00 0.2712E+00
0.2762E+00 0.2806E+00 0.2844E+00 0.2875E+00 0.2902E+00 0.2924E+00 0.2941E+00
0.2955E+00 0.2966E+00 0.2975E+00 0.2981E+00 0.2986E+00 0.2990E+00 0.2993E+00
0.2995E+00 0.2996E+00 0.2998E+00 0.2998E+00 0.2999E+00 0.2999E+00 0.2999E+00
0.2999E+00 0.2999E+00 0.2998E+00 0.2995E+00 0.2992E+00 0.2985E+00 0.2972E+00
0.2948E+00 0.2904E+00 0.2820E+00 0.2686E+00 0.2491E+00 0.2219E+00 0.1869E+00
0.1474E+00 0.1085E+00 0.7511E-01 0.4945E-01 0.3134E-01 0.1929E-01 0.1159E-01
0.6825E-02 0.3944E-02 0.2239E-02 0.1249E-02 0.6833E-03 0.3643E-03 0.1837E-03
0.7624E-04
Values of PDE component i = 3
0.6162E-07 0.1377E-06 0.2513E-06 0.4520E-06 0.8610E-06 0.1779E-05 0.3932E-05
0.8985E-05 0.2057E-04 0.4616E-04 0.1003E-03 0.2094E-03 0.4185E-03 0.7992E-03
0.1457E-02 0.2534E-02 0.4208E-02 0.6681E-02 0.1016E-01 0.1485E-01 0.2091E-01
0.2846E-01 0.3758E-01 0.4830E-01 0.6060E-01 0.7441E-01 0.8966E-01 0.1062E+00
0.1240E+00 0.1428E+00 0.1626E+00 0.1831E+00 0.2045E+00 0.2264E+00 0.2488E+00
0.2714E+00 0.2941E+00 0.3166E+00 0.3384E+00 0.3594E+00 0.3791E+00 0.3974E+00
0.4141E+00 0.4290E+00 0.4422E+00 0.4536E+00 0.4633E+00 0.4714E+00 0.4781E+00
0.4834E+00 0.4877E+00 0.4910E+00 0.4935E+00 0.4954E+00 0.4968E+00 0.4978E+00
0.4985E+00 0.4990E+00 0.4993E+00 0.4996E+00 0.4997E+00 0.4998E+00 0.4999E+00
0.4999E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00
0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5001E+00 0.5002E+00 0.5007E+00
0.5022E+00 0.5016E+00 0.4950E+00 0.4878E+00 0.4672E+00 0.4132E+00 0.3339E+00
0.2415E+00 0.1512E+00 0.8188E-01 0.3937E-01 0.1726E-01 0.7067E-02 0.2745E-02
0.1022E-02 0.3663E-03 0.1269E-03 0.4241E-04 0.1362E-04 0.4154E-05 0.1175E-05
0.2869E-06
Final statistics for mf = 21: 30 steps, 45 res, 11 jacobians,
rwork size = 5368, iwork size = 317
Final output is correct to within 0.14E+02 times local error tolerance.
******************************************************************************************
Run with rtol = 0.1E-02 atol = 0.1E-02 mf = 22
At time t = 0.10000E+00 current h = 0.17219E-01 current order = 2 current nst = 20
At time t = 0.20000E+00 current h = 0.33216E-01 current order = 2 current nst = 24
At time t = 0.30000E+00 current h = 0.33216E-01 current order = 2 current nst = 27
At time t = 0.40000E+00 current h = 0.33216E-01 current order = 2 current nst = 30
Values of PDE component i = 1
0.1713E-02 0.3441E-02 0.5199E-02 0.7001E-02 0.8861E-02 0.1079E-01 0.1280E-01
0.1490E-01 0.1710E-01 0.1940E-01 0.2181E-01 0.2433E-01 0.2695E-01 0.2968E-01
0.3252E-01 0.3545E-01 0.3846E-01 0.4156E-01 0.4473E-01 0.4797E-01 0.5126E-01
0.5460E-01 0.5797E-01 0.6138E-01 0.6481E-01 0.6826E-01 0.7172E-01 0.7520E-01
0.7868E-01 0.8216E-01 0.8565E-01 0.8915E-01 0.9264E-01 0.9614E-01 0.9964E-01
0.1031E+00 0.1066E+00 0.1102E+00 0.1137E+00 0.1172E+00 0.1207E+00 0.1243E+00
0.1278E+00 0.1314E+00 0.1349E+00 0.1384E+00 0.1419E+00 0.1453E+00 0.1487E+00
0.1520E+00 0.1552E+00 0.1584E+00 0.1614E+00 0.1643E+00 0.1670E+00 0.1696E+00
0.1720E+00 0.1742E+00 0.1762E+00 0.1780E+00 0.1796E+00 0.1810E+00 0.1820E+00
0.1829E+00 0.1834E+00 0.1837E+00 0.1836E+00 0.1832E+00 0.1825E+00 0.1814E+00
0.1798E+00 0.1779E+00 0.1755E+00 0.1726E+00 0.1691E+00 0.1651E+00 0.1605E+00
0.1552E+00 0.1493E+00 0.1426E+00 0.1351E+00 0.1270E+00 0.1181E+00 0.1087E+00
0.9897E-01 0.8921E-01 0.7968E-01 0.7060E-01 0.6208E-01 0.5416E-01 0.4685E-01
0.4011E-01 0.3390E-01 0.2816E-01 0.2283E-01 0.1785E-01 0.1314E-01 0.8644E-02
0.4287E-02
Values of PDE component i = 2
0.8220E-05 0.1912E-04 0.3600E-04 0.6353E-04 0.1086E-03 0.1813E-03 0.2965E-03
0.4746E-03 0.7437E-03 0.1141E-02 0.1711E-02 0.2511E-02 0.3603E-02 0.5056E-02
0.6939E-02 0.9317E-02 0.1225E-01 0.1577E-01 0.1992E-01 0.2470E-01 0.3010E-01
0.3611E-01 0.4268E-01 0.4978E-01 0.5735E-01 0.6535E-01 0.7372E-01 0.8242E-01
0.9140E-01 0.1006E+00 0.1100E+00 0.1196E+00 0.1293E+00 0.1391E+00 0.1490E+00
0.1590E+00 0.1691E+00 0.1792E+00 0.1892E+00 0.1991E+00 0.2088E+00 0.2183E+00
0.2275E+00 0.2362E+00 0.2444E+00 0.2521E+00 0.2591E+00 0.2655E+00 0.2712E+00
0.2763E+00 0.2806E+00 0.2844E+00 0.2876E+00 0.2902E+00 0.2924E+00 0.2941E+00
0.2955E+00 0.2966E+00 0.2975E+00 0.2981E+00 0.2986E+00 0.2990E+00 0.2993E+00
0.2995E+00 0.2997E+00 0.2998E+00 0.2998E+00 0.2999E+00 0.2999E+00 0.2999E+00
0.2999E+00 0.2999E+00 0.2998E+00 0.2995E+00 0.2992E+00 0.2984E+00 0.2971E+00
0.2946E+00 0.2900E+00 0.2819E+00 0.2688E+00 0.2494E+00 0.2221E+00 0.1872E+00
0.1478E+00 0.1089E+00 0.7549E-01 0.4976E-01 0.3156E-01 0.1943E-01 0.1168E-01
0.6879E-02 0.3975E-02 0.2257E-02 0.1259E-02 0.6888E-03 0.3673E-03 0.1853E-03
0.7689E-04
Values of PDE component i = 3
0.6430E-08 0.2134E-07 0.6312E-07 0.1798E-06 0.4960E-06 0.1323E-05 0.3404E-05
0.8433E-05 0.2008E-04 0.4585E-04 0.1003E-03 0.2099E-03 0.4196E-03 0.8010E-03
0.1459E-02 0.2537E-02 0.4212E-02 0.6685E-02 0.1017E-01 0.1486E-01 0.2092E-01
0.2848E-01 0.3762E-01 0.4836E-01 0.6068E-01 0.7453E-01 0.8981E-01 0.1064E+00
0.1242E+00 0.1431E+00 0.1628E+00 0.1835E+00 0.2048E+00 0.2267E+00 0.2490E+00
0.2716E+00 0.2943E+00 0.3167E+00 0.3385E+00 0.3595E+00 0.3792E+00 0.3975E+00
0.4141E+00 0.4290E+00 0.4422E+00 0.4536E+00 0.4633E+00 0.4714E+00 0.4780E+00
0.4834E+00 0.4877E+00 0.4910E+00 0.4935E+00 0.4954E+00 0.4968E+00 0.4978E+00
0.4985E+00 0.4990E+00 0.4993E+00 0.4996E+00 0.4997E+00 0.4998E+00 0.4999E+00
0.4999E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00
0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5001E+00 0.5002E+00 0.5008E+00
0.5024E+00 0.5018E+00 0.4949E+00 0.4881E+00 0.4679E+00 0.4136E+00 0.3344E+00
0.2425E+00 0.1521E+00 0.8249E-01 0.3969E-01 0.1741E-01 0.7129E-02 0.2769E-02
0.1031E-02 0.3705E-03 0.1289E-03 0.4358E-04 0.1433E-04 0.4592E-05 0.1427E-05
0.4012E-06
Final statistics for mf = 22: 30 steps, 155 res, 11 jacobians,
rwork size = 5368, iwork size = 317
Final output is correct to within 0.14E+02 times local error tolerance.
******************************************************************************************
Run with rtol = 0.1E-05 atol = 0.1E-05 mf = 11
At time t = 0.10000E+00 current h = 0.79980E-02 current order = 4 current nst = 60
At time t = 0.20000E+00 current h = 0.10116E-01 current order = 4 current nst = 71
At time t = 0.30000E+00 current h = 0.12090E-01 current order = 4 current nst = 89
At time t = 0.40000E+00 current h = 0.12812E-01 current order = 4 current nst = 106
Values of PDE component i = 1
0.1710E-02 0.3434E-02 0.5188E-02 0.6985E-02 0.8839E-02 0.1076E-01 0.1277E-01
0.1486E-01 0.1705E-01 0.1934E-01 0.2174E-01 0.2425E-01 0.2687E-01 0.2960E-01
0.3243E-01 0.3536E-01 0.3838E-01 0.4149E-01 0.4468E-01 0.4793E-01 0.5124E-01
0.5460E-01 0.5799E-01 0.6143E-01 0.6489E-01 0.6836E-01 0.7186E-01 0.7536E-01
0.7887E-01 0.8239E-01 0.8591E-01 0.8943E-01 0.9295E-01 0.9647E-01 0.9999E-01
0.1035E+00 0.1070E+00 0.1106E+00 0.1141E+00 0.1176E+00 0.1211E+00 0.1246E+00
0.1281E+00 0.1316E+00 0.1350E+00 0.1384E+00 0.1418E+00 0.1452E+00 0.1485E+00
0.1517E+00 0.1549E+00 0.1580E+00 0.1609E+00 0.1638E+00 0.1665E+00 0.1691E+00
0.1715E+00 0.1737E+00 0.1758E+00 0.1776E+00 0.1793E+00 0.1806E+00 0.1818E+00
0.1827E+00 0.1833E+00 0.1836E+00 0.1836E+00 0.1832E+00 0.1825E+00 0.1814E+00
0.1799E+00 0.1780E+00 0.1756E+00 0.1727E+00 0.1693E+00 0.1653E+00 0.1606E+00
0.1554E+00 0.1494E+00 0.1427E+00 0.1353E+00 0.1271E+00 0.1183E+00 0.1089E+00
0.9916E-01 0.8935E-01 0.7978E-01 0.7067E-01 0.6212E-01 0.5420E-01 0.4688E-01
0.4015E-01 0.3394E-01 0.2820E-01 0.2286E-01 0.1788E-01 0.1316E-01 0.8659E-02
0.4295E-02
Values of PDE component i = 2
0.7174E-05 0.1708E-04 0.3312E-04 0.6016E-04 0.1053E-03 0.1792E-03 0.2967E-03
0.4789E-03 0.7536E-03 0.1157E-02 0.1734E-02 0.2538E-02 0.3631E-02 0.5078E-02
0.6948E-02 0.9306E-02 0.1221E-01 0.1572E-01 0.1985E-01 0.2462E-01 0.3004E-01
0.3608E-01 0.4271E-01 0.4988E-01 0.5755E-01 0.6566E-01 0.7415E-01 0.8298E-01
0.9208E-01 0.1014E+00 0.1109E+00 0.1206E+00 0.1303E+00 0.1401E+00 0.1500E+00
0.1599E+00 0.1697E+00 0.1794E+00 0.1891E+00 0.1986E+00 0.2079E+00 0.2170E+00
0.2258E+00 0.2343E+00 0.2425E+00 0.2501E+00 0.2573E+00 0.2639E+00 0.2700E+00
0.2754E+00 0.2802E+00 0.2843E+00 0.2878E+00 0.2907E+00 0.2931E+00 0.2949E+00
0.2964E+00 0.2975E+00 0.2983E+00 0.2988E+00 0.2992E+00 0.2995E+00 0.2997E+00
0.2998E+00 0.2999E+00 0.2999E+00 0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00
0.2999E+00 0.2999E+00 0.2997E+00 0.2994E+00 0.2989E+00 0.2980E+00 0.2964E+00
0.2937E+00 0.2890E+00 0.2814E+00 0.2693E+00 0.2509E+00 0.2245E+00 0.1899E+00
0.1499E+00 0.1099E+00 0.7540E-01 0.4903E-01 0.3061E-01 0.1852E-01 0.1091E-01
0.6277E-02 0.3530E-02 0.1941E-02 0.1042E-02 0.5461E-03 0.2774E-03 0.1334E-03
0.5328E-04
Values of PDE component i = 3
0.1970E-09 0.1996E-08 0.1198E-07 0.5563E-07 0.2186E-06 0.7563E-06 0.2357E-05
0.6709E-05 0.1762E-04 0.4304E-04 0.9826E-04 0.2107E-03 0.4262E-03 0.8157E-03
0.1482E-02 0.2562E-02 0.4229E-02 0.6681E-02 0.1013E-01 0.1479E-01 0.2084E-01
0.2843E-01 0.3766E-01 0.4855E-01 0.6109E-01 0.7522E-01 0.9082E-01 0.1078E+00
0.1259E+00 0.1450E+00 0.1650E+00 0.1857E+00 0.2069E+00 0.2284E+00 0.2500E+00
0.2717E+00 0.2932E+00 0.3143E+00 0.3350E+00 0.3550E+00 0.3741E+00 0.3922E+00
0.4092E+00 0.4248E+00 0.4389E+00 0.4514E+00 0.4623E+00 0.4715E+00 0.4791E+00
0.4852E+00 0.4899E+00 0.4933E+00 0.4958E+00 0.4974E+00 0.4985E+00 0.4992E+00
0.4996E+00 0.4998E+00 0.4999E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00
0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00
0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.4998E+00
0.4994E+00 0.4982E+00 0.4949E+00 0.4861E+00 0.4652E+00 0.4219E+00 0.3479E+00
0.2496E+00 0.1516E+00 0.7801E-01 0.3480E-01 0.1387E-01 0.5059E-02 0.1712E-02
0.5396E-03 0.1582E-03 0.4287E-04 0.1061E-04 0.2351E-05 0.4522E-06 0.7093E-07
0.7792E-08
Final statistics for mf = 11: 106 steps, 148 res, 23 jacobians,
rwork size = 7447, iwork size = 317
Final output is correct to within 0.67E+01 times local error tolerance.
******************************************************************************************
Run with rtol = 0.1E-05 atol = 0.1E-05 mf = 12
At time t = 0.10000E+00 current h = 0.64185E-02 current order = 3 current nst = 61
At time t = 0.20000E+00 current h = 0.13037E-01 current order = 4 current nst = 71
At time t = 0.30000E+00 current h = 0.68710E-02 current order = 3 current nst = 89
At time t = 0.40000E+00 current h = 0.84070E-02 current order = 3 current nst = 100
Values of PDE component i = 1
0.1710E-02 0.3434E-02 0.5188E-02 0.6985E-02 0.8839E-02 0.1076E-01 0.1276E-01
0.1486E-01 0.1705E-01 0.1934E-01 0.2174E-01 0.2425E-01 0.2687E-01 0.2960E-01
0.3243E-01 0.3536E-01 0.3838E-01 0.4149E-01 0.4467E-01 0.4793E-01 0.5124E-01
0.5460E-01 0.5800E-01 0.6142E-01 0.6489E-01 0.6836E-01 0.7186E-01 0.7535E-01
0.7888E-01 0.8238E-01 0.8591E-01 0.8942E-01 0.9295E-01 0.9646E-01 0.1000E+00
0.1035E+00 0.1070E+00 0.1105E+00 0.1141E+00 0.1176E+00 0.1211E+00 0.1246E+00
0.1281E+00 0.1316E+00 0.1350E+00 0.1384E+00 0.1418E+00 0.1452E+00 0.1485E+00
0.1517E+00 0.1549E+00 0.1580E+00 0.1609E+00 0.1638E+00 0.1665E+00 0.1691E+00
0.1715E+00 0.1737E+00 0.1758E+00 0.1776E+00 0.1793E+00 0.1806E+00 0.1818E+00
0.1827E+00 0.1833E+00 0.1836E+00 0.1836E+00 0.1832E+00 0.1825E+00 0.1814E+00
0.1799E+00 0.1780E+00 0.1756E+00 0.1727E+00 0.1693E+00 0.1653E+00 0.1606E+00
0.1554E+00 0.1494E+00 0.1427E+00 0.1353E+00 0.1271E+00 0.1183E+00 0.1089E+00
0.9916E-01 0.8935E-01 0.7978E-01 0.7067E-01 0.6212E-01 0.5420E-01 0.4688E-01
0.4015E-01 0.3394E-01 0.2820E-01 0.2286E-01 0.1788E-01 0.1316E-01 0.8659E-02
0.4295E-02
Values of PDE component i = 2
0.7174E-05 0.1708E-04 0.3312E-04 0.6016E-04 0.1053E-03 0.1792E-03 0.2967E-03
0.4789E-03 0.7536E-03 0.1157E-02 0.1734E-02 0.2538E-02 0.3631E-02 0.5078E-02
0.6948E-02 0.9306E-02 0.1221E-01 0.1572E-01 0.1985E-01 0.2462E-01 0.3004E-01
0.3608E-01 0.4271E-01 0.4988E-01 0.5755E-01 0.6566E-01 0.7415E-01 0.8298E-01
0.9208E-01 0.1014E+00 0.1109E+00 0.1206E+00 0.1303E+00 0.1401E+00 0.1500E+00
0.1599E+00 0.1697E+00 0.1794E+00 0.1891E+00 0.1986E+00 0.2079E+00 0.2170E+00
0.2258E+00 0.2343E+00 0.2425E+00 0.2501E+00 0.2573E+00 0.2639E+00 0.2700E+00
0.2754E+00 0.2802E+00 0.2843E+00 0.2878E+00 0.2907E+00 0.2931E+00 0.2949E+00
0.2964E+00 0.2975E+00 0.2983E+00 0.2988E+00 0.2992E+00 0.2995E+00 0.2997E+00
0.2998E+00 0.2999E+00 0.2999E+00 0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00
0.2999E+00 0.2999E+00 0.2997E+00 0.2994E+00 0.2989E+00 0.2980E+00 0.2964E+00
0.2937E+00 0.2890E+00 0.2814E+00 0.2693E+00 0.2509E+00 0.2245E+00 0.1899E+00
0.1499E+00 0.1099E+00 0.7540E-01 0.4902E-01 0.3061E-01 0.1852E-01 0.1091E-01
0.6278E-02 0.3530E-02 0.1941E-02 0.1042E-02 0.5461E-03 0.2775E-03 0.1334E-03
0.5329E-04
Values of PDE component i = 3
0.2003E-09 0.2003E-08 0.1198E-07 0.5562E-07 0.2185E-06 0.7561E-06 0.2356E-05
0.6708E-05 0.1762E-04 0.4303E-04 0.9826E-04 0.2107E-03 0.4262E-03 0.8157E-03
0.1482E-02 0.2562E-02 0.4229E-02 0.6681E-02 0.1013E-01 0.1479E-01 0.2084E-01
0.2843E-01 0.3766E-01 0.4855E-01 0.6109E-01 0.7522E-01 0.9082E-01 0.1078E+00
0.1259E+00 0.1450E+00 0.1650E+00 0.1857E+00 0.2069E+00 0.2284E+00 0.2500E+00
0.2717E+00 0.2932E+00 0.3143E+00 0.3350E+00 0.3550E+00 0.3741E+00 0.3922E+00
0.4092E+00 0.4248E+00 0.4389E+00 0.4514E+00 0.4623E+00 0.4715E+00 0.4791E+00
0.4852E+00 0.4899E+00 0.4933E+00 0.4958E+00 0.4974E+00 0.4985E+00 0.4992E+00
0.4996E+00 0.4998E+00 0.4999E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00
0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00
0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.4998E+00
0.4994E+00 0.4982E+00 0.4949E+00 0.4861E+00 0.4652E+00 0.4219E+00 0.3479E+00
0.2496E+00 0.1516E+00 0.7801E-01 0.3480E-01 0.1387E-01 0.5061E-02 0.1713E-02
0.5401E-03 0.1584E-03 0.4295E-04 0.1063E-04 0.2361E-05 0.4556E-06 0.7202E-07
0.8103E-08
Final statistics for mf = 12: 100 steps, 353 res, 22 jacobians,
rwork size = 7447, iwork size = 317
Final output is correct to within 0.12E+02 times local error tolerance.
******************************************************************************************
Run with rtol = 0.1E-05 atol = 0.1E-05 mf = 21
At time t = 0.10000E+00 current h = 0.57520E-02 current order = 4 current nst = 72
At time t = 0.20000E+00 current h = 0.92622E-02 current order = 5 current nst = 85
At time t = 0.30000E+00 current h = 0.12274E-01 current order = 5 current nst = 95
At time t = 0.40000E+00 current h = 0.12274E-01 current order = 5 current nst = 103
Values of PDE component i = 1
0.1710E-02 0.3434E-02 0.5188E-02 0.6985E-02 0.8839E-02 0.1076E-01 0.1277E-01
0.1486E-01 0.1705E-01 0.1934E-01 0.2174E-01 0.2425E-01 0.2687E-01 0.2960E-01
0.3243E-01 0.3536E-01 0.3838E-01 0.4149E-01 0.4468E-01 0.4793E-01 0.5124E-01
0.5460E-01 0.5799E-01 0.6143E-01 0.6489E-01 0.6836E-01 0.7186E-01 0.7536E-01
0.7887E-01 0.8239E-01 0.8591E-01 0.8943E-01 0.9295E-01 0.9647E-01 0.9999E-01
0.1035E+00 0.1070E+00 0.1106E+00 0.1141E+00 0.1176E+00 0.1211E+00 0.1246E+00
0.1281E+00 0.1316E+00 0.1350E+00 0.1384E+00 0.1418E+00 0.1452E+00 0.1485E+00
0.1517E+00 0.1549E+00 0.1580E+00 0.1609E+00 0.1638E+00 0.1665E+00 0.1691E+00
0.1715E+00 0.1737E+00 0.1758E+00 0.1776E+00 0.1793E+00 0.1806E+00 0.1818E+00
0.1827E+00 0.1833E+00 0.1836E+00 0.1836E+00 0.1832E+00 0.1825E+00 0.1814E+00
0.1799E+00 0.1780E+00 0.1756E+00 0.1727E+00 0.1693E+00 0.1653E+00 0.1606E+00
0.1554E+00 0.1494E+00 0.1427E+00 0.1353E+00 0.1271E+00 0.1183E+00 0.1089E+00
0.9916E-01 0.8935E-01 0.7978E-01 0.7067E-01 0.6212E-01 0.5420E-01 0.4688E-01
0.4015E-01 0.3394E-01 0.2820E-01 0.2286E-01 0.1788E-01 0.1316E-01 0.8659E-02
0.4295E-02
Values of PDE component i = 2
0.7174E-05 0.1708E-04 0.3312E-04 0.6016E-04 0.1053E-03 0.1792E-03 0.2967E-03
0.4789E-03 0.7536E-03 0.1157E-02 0.1734E-02 0.2538E-02 0.3631E-02 0.5078E-02
0.6948E-02 0.9306E-02 0.1221E-01 0.1572E-01 0.1985E-01 0.2462E-01 0.3004E-01
0.3608E-01 0.4271E-01 0.4988E-01 0.5755E-01 0.6566E-01 0.7415E-01 0.8298E-01
0.9208E-01 0.1014E+00 0.1109E+00 0.1206E+00 0.1303E+00 0.1401E+00 0.1500E+00
0.1599E+00 0.1697E+00 0.1794E+00 0.1891E+00 0.1986E+00 0.2079E+00 0.2170E+00
0.2258E+00 0.2343E+00 0.2425E+00 0.2501E+00 0.2573E+00 0.2639E+00 0.2700E+00
0.2754E+00 0.2802E+00 0.2843E+00 0.2878E+00 0.2907E+00 0.2931E+00 0.2949E+00
0.2964E+00 0.2975E+00 0.2983E+00 0.2988E+00 0.2993E+00 0.2995E+00 0.2997E+00
0.2998E+00 0.2999E+00 0.2999E+00 0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00
0.2999E+00 0.2999E+00 0.2997E+00 0.2994E+00 0.2989E+00 0.2980E+00 0.2964E+00
0.2937E+00 0.2890E+00 0.2814E+00 0.2693E+00 0.2509E+00 0.2245E+00 0.1899E+00
0.1499E+00 0.1099E+00 0.7540E-01 0.4903E-01 0.3061E-01 0.1852E-01 0.1091E-01
0.6277E-02 0.3530E-02 0.1941E-02 0.1042E-02 0.5460E-03 0.2774E-03 0.1333E-03
0.5327E-04
Values of PDE component i = 3
0.1721E-09 0.1938E-08 0.1186E-07 0.5543E-07 0.2183E-06 0.7559E-06 0.2356E-05
0.6708E-05 0.1762E-04 0.4304E-04 0.9826E-04 0.2107E-03 0.4262E-03 0.8157E-03
0.1482E-02 0.2562E-02 0.4228E-02 0.6681E-02 0.1013E-01 0.1479E-01 0.2084E-01
0.2843E-01 0.3766E-01 0.4855E-01 0.6109E-01 0.7522E-01 0.9082E-01 0.1078E+00
0.1259E+00 0.1450E+00 0.1650E+00 0.1857E+00 0.2069E+00 0.2284E+00 0.2500E+00
0.2717E+00 0.2932E+00 0.3143E+00 0.3350E+00 0.3550E+00 0.3741E+00 0.3922E+00
0.4092E+00 0.4248E+00 0.4389E+00 0.4514E+00 0.4623E+00 0.4715E+00 0.4791E+00
0.4852E+00 0.4899E+00 0.4933E+00 0.4958E+00 0.4974E+00 0.4985E+00 0.4992E+00
0.4996E+00 0.4998E+00 0.4999E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00
0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00
0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.4998E+00
0.4994E+00 0.4982E+00 0.4949E+00 0.4861E+00 0.4652E+00 0.4218E+00 0.3479E+00
0.2497E+00 0.1517E+00 0.7801E-01 0.3480E-01 0.1387E-01 0.5057E-02 0.1711E-02
0.5392E-03 0.1581E-03 0.4283E-04 0.1060E-04 0.2350E-05 0.4530E-06 0.7165E-07
0.8130E-08
Final statistics for mf = 21: 103 steps, 122 res, 17 jacobians,
rwork size = 5368, iwork size = 317
Final output is correct to within 0.11E+02 times local error tolerance.
******************************************************************************************
Run with rtol = 0.1E-05 atol = 0.1E-05 mf = 22
At time t = 0.10000E+00 current h = 0.57538E-02 current order = 4 current nst = 72
At time t = 0.20000E+00 current h = 0.92575E-02 current order = 5 current nst = 85
At time t = 0.30000E+00 current h = 0.12294E-01 current order = 5 current nst = 95
At time t = 0.40000E+00 current h = 0.12294E-01 current order = 5 current nst = 103
Values of PDE component i = 1
0.1710E-02 0.3434E-02 0.5188E-02 0.6985E-02 0.8839E-02 0.1076E-01 0.1277E-01
0.1486E-01 0.1705E-01 0.1934E-01 0.2174E-01 0.2425E-01 0.2687E-01 0.2960E-01
0.3243E-01 0.3536E-01 0.3838E-01 0.4149E-01 0.4468E-01 0.4793E-01 0.5124E-01
0.5460E-01 0.5799E-01 0.6143E-01 0.6489E-01 0.6836E-01 0.7186E-01 0.7536E-01
0.7887E-01 0.8239E-01 0.8591E-01 0.8943E-01 0.9295E-01 0.9647E-01 0.9999E-01
0.1035E+00 0.1070E+00 0.1106E+00 0.1141E+00 0.1176E+00 0.1211E+00 0.1246E+00
0.1281E+00 0.1316E+00 0.1350E+00 0.1384E+00 0.1418E+00 0.1452E+00 0.1485E+00
0.1517E+00 0.1549E+00 0.1580E+00 0.1609E+00 0.1638E+00 0.1665E+00 0.1691E+00
0.1715E+00 0.1737E+00 0.1758E+00 0.1776E+00 0.1793E+00 0.1806E+00 0.1818E+00
0.1827E+00 0.1833E+00 0.1836E+00 0.1836E+00 0.1832E+00 0.1825E+00 0.1814E+00
0.1799E+00 0.1780E+00 0.1756E+00 0.1727E+00 0.1693E+00 0.1653E+00 0.1606E+00
0.1554E+00 0.1494E+00 0.1427E+00 0.1353E+00 0.1271E+00 0.1183E+00 0.1089E+00
0.9916E-01 0.8935E-01 0.7978E-01 0.7067E-01 0.6212E-01 0.5420E-01 0.4688E-01
0.4015E-01 0.3394E-01 0.2820E-01 0.2286E-01 0.1788E-01 0.1316E-01 0.8659E-02
0.4295E-02
Values of PDE component i = 2
0.7174E-05 0.1708E-04 0.3312E-04 0.6016E-04 0.1053E-03 0.1792E-03 0.2967E-03
0.4789E-03 0.7536E-03 0.1157E-02 0.1734E-02 0.2538E-02 0.3631E-02 0.5078E-02
0.6948E-02 0.9306E-02 0.1221E-01 0.1572E-01 0.1985E-01 0.2462E-01 0.3004E-01
0.3608E-01 0.4271E-01 0.4988E-01 0.5755E-01 0.6566E-01 0.7415E-01 0.8298E-01
0.9208E-01 0.1014E+00 0.1109E+00 0.1206E+00 0.1303E+00 0.1401E+00 0.1500E+00
0.1599E+00 0.1697E+00 0.1794E+00 0.1891E+00 0.1986E+00 0.2079E+00 0.2170E+00
0.2258E+00 0.2343E+00 0.2425E+00 0.2501E+00 0.2573E+00 0.2639E+00 0.2700E+00
0.2754E+00 0.2802E+00 0.2843E+00 0.2878E+00 0.2907E+00 0.2931E+00 0.2949E+00
0.2964E+00 0.2975E+00 0.2983E+00 0.2988E+00 0.2993E+00 0.2995E+00 0.2997E+00
0.2998E+00 0.2999E+00 0.2999E+00 0.3000E+00 0.3000E+00 0.3000E+00 0.3000E+00
0.2999E+00 0.2999E+00 0.2997E+00 0.2994E+00 0.2989E+00 0.2980E+00 0.2964E+00
0.2937E+00 0.2890E+00 0.2814E+00 0.2693E+00 0.2509E+00 0.2245E+00 0.1899E+00
0.1499E+00 0.1099E+00 0.7540E-01 0.4903E-01 0.3061E-01 0.1852E-01 0.1091E-01
0.6277E-02 0.3530E-02 0.1941E-02 0.1042E-02 0.5460E-03 0.2774E-03 0.1333E-03
0.5327E-04
Values of PDE component i = 3
0.1916E-09 0.1973E-08 0.1191E-07 0.5547E-07 0.2183E-06 0.7558E-06 0.2356E-05
0.6708E-05 0.1762E-04 0.4304E-04 0.9826E-04 0.2107E-03 0.4262E-03 0.8157E-03
0.1482E-02 0.2562E-02 0.4228E-02 0.6681E-02 0.1013E-01 0.1479E-01 0.2084E-01
0.2843E-01 0.3766E-01 0.4855E-01 0.6109E-01 0.7522E-01 0.9082E-01 0.1078E+00
0.1259E+00 0.1450E+00 0.1650E+00 0.1857E+00 0.2069E+00 0.2284E+00 0.2500E+00
0.2717E+00 0.2932E+00 0.3143E+00 0.3350E+00 0.3550E+00 0.3741E+00 0.3922E+00
0.4092E+00 0.4248E+00 0.4389E+00 0.4514E+00 0.4623E+00 0.4715E+00 0.4791E+00
0.4852E+00 0.4899E+00 0.4933E+00 0.4958E+00 0.4974E+00 0.4985E+00 0.4992E+00
0.4996E+00 0.4998E+00 0.4999E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00
0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00
0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.5000E+00 0.4998E+00
0.4994E+00 0.4982E+00 0.4949E+00 0.4861E+00 0.4652E+00 0.4218E+00 0.3479E+00
0.2497E+00 0.1517E+00 0.7801E-01 0.3480E-01 0.1387E-01 0.5057E-02 0.1711E-02
0.5392E-03 0.1581E-03 0.4283E-04 0.1060E-04 0.2350E-05 0.4530E-06 0.7161E-07
0.8102E-08
Final statistics for mf = 22: 103 steps, 292 res, 17 jacobians,
rwork size = 5368, iwork size = 317
Final output is correct to within 0.12E+02 times local error tolerance.
******************************************************************************************
Run completed: 0 errors encountered
==========Source and Output for LSODIS Demonstration Program====================
c-----------------------------------------------------------------------
c Demonstration program for the SLSODIS package.
c This is the version of 15 June 2001.
c
c This version is in single precision.
c
c This program solves a semi-discretized form of the Burgers equation,
c
c u = -(u*u/2) + eta * u
c t x xx
c
c for -1 .le. x .le. 1, t .ge. 0.
c Here eta = 0.05.
c Boundary conditions: u(-1,t) = u(1,t) and du/dx(-1,t) = du/dx(1,t).
c Initial profile: square wave
c u(0,x) = 0 for 1/2 .lt. abs(x) .le. 1
c u(0,x) = 1/2 for abs(x) = 1/2
c u(0,x) = 1 for 0 .le. abs(x) .lt. 1/2
c
c An ODE system is generated by a simplified Galerkin treatment
c of the spatial variable x.
c
c Reference:
c R. C. Y. Chin, G. W. Hedstrom, and K. E. Karlsson,
c A Simplified Galerkin Method for Hyperbolic Equations,
c Math. Comp., vol. 33, no. 146 (April 1979), pp. 647-658.
c
c The problem is run with the SLSODIS package with a 12-node mesh,
c for various appropriate values of the method flag mf.
c Output is on unit lout, set to 6 in a data statement below.
c
c Problem specific data:
c npts = number of unknowns (npts = 0 mod 4)
c nnz = number of non-zeros in Jacobian before fill in
c nnza = number of non-zeros in Jacobian after fill in
c lrwk = length of real work array (taking into account fill in)
c liwk = length of integer work array
c ipia = pointer to ia in iw (ia(j) = iw(ipia+j-1)
c ipja = pointer to ja in iw (ja(j) = iw(ipja+j-1)
c ipic = pointer to ic in iw array (ic(j) = iw(ipic+j-1))
c ipjc = pointer to jc in iw array (jc(j) = iw(ipjc+j-1))
c-----------------------------------------------------------------------
parameter (npts = 12, nnz = 3*npts, nnza = 5*npts)
parameter (lrwk = 20+3*nnza+28*npts)
parameter (liwk = 32+2*nnza+2*npts)
parameter (ipia = 31, ipja = 31+npts+1)
parameter (ll = 32+npts+nnz, ipic = ll,ipjc = ll+npts+1)
c
external res, addasp, jacsp
integer i, io, istate, itol, iw, j, lout, lrw, liw, lyh,
1 meth, miter, mf, moss, n, nout, nerr, n14, n34
real eta, delta, r4d, eodsq, a, b, t, tout, tlast,
1 tinit, errfac
real atol, rtol, rw, y, ydoti, elkup
real zero, fourth, half, one, hun
dimension y(npts), ydoti(npts), tout(4), atol(2), rtol(2)
dimension rw(lrwk), iw(liwk)
c Pass problem parameters in the Common block test1.
common /test1/ r4d, eodsq
c
c Set problem parameters and run parameters
data eta/0.05e0/, a/-1.0e0/, b/1.0e0/
data zero/0.0e0/, fourth/0.25e0/, half/0.5e0/, one/1.0e0/,
1 hun/100.0e0/
data tinit/0.0e0/, tlast/0.4e0/
data tout/0.10e0, 0.20e0, 0.30e0, 0.40e0/
data lout/6/, nout/4/
data itol/1/, rtol/1.0e-3, 1.0e-6/, atol/1.0e-3, 1.0e-6/
c
nerr = 0
lrw = lrwk
liw = liwk
c
c Compute the mesh width delta and other parameters.
delta = (b - a)/npts
r4d = fourth/delta
eodsq = eta/delta**2
n14 = npts/4 + 1
n34 = 3 * (npts/4) + 1
n = npts
c
c Set the initial profile (for output purposes only).
do 10 i = 1,n
10 y(i) = zero
y(n14) = half
do 20 i = n14+1,n34-1
20 y(i) = one
y(n34) = half
c
write(lout,1000)
write(lout,1100) eta,a,b,tinit,tlast,n
write(lout,1200) (y(i), i=1,n)
c
c Set the initial sparse data structures for coefficient matrix A
c and the Jacobian matrix C
call struct(iw(ipia), iw(ipja), iw(ipic), iw(ipjc), n)
c
c The j loop is over error tolerances.
do 200 j = 1,2
c
c This method flag loop is for demonstration only.
do 200 moss = 0,4
do 100 meth = 1,2
do 100 miter = 1,2
35 mf = 100*moss + 10*meth + miter
c
c Set the initial profile.
do 40 i = 1,n
40 y(i) = zero
y(n14) = half
do 50 i = n14+1,n34-1
50 y(i) = one
y(n34) = half
c
t = tinit
istate = 0
c
write(lout,1500) itol, rtol(j), atol(j), mf
c
c output loop for each case
do 80 io = 1,nout
c
c Call SLSODIS and print results.
call slsodis (res, addasp, jacsp, n, y, ydoti, t,
1 tout(io), itol, rtol(j), atol(j), 1, istate, 0,
2 rw, lrw, iw, liw, mf)
write(lout,2000) t, rw(11), iw(14), (y(i), i=1,n)
c
c If istate is not 2 on return, print message and go to next case.
if (istate .ne. 2) then
write(lout,4000) mf, t, istate
nerr = nerr + 1
go to 100
endif
80 continue
write(lout,3000) mf, iw(11), iw(12), iw(13),
1 iw(17), iw(18), iw(20), iw(21)
c
c Estimate final error and print result.
lyh = iw(22)
errfac = elkup(n, y, rw(lyh), itol, rtol(j), atol(j), lout)
if (errfac .lt. hun) then
write(lout,5000) errfac
else
write(lout,5001) errfac
nerr = nerr + 1
endif
100 continue
200 continue
c
write(lout,6000) nerr
stop
c
1000 format(20x,' Demonstration Program for SLSODIS' )
1100 format(//10x,'-- Simplified Galerkin solution of ',
1 'Burgers equation --'///
1 13x,'Diffusion coefficient is eta =',e10.2/
1 13x,'Uniform mesh on interval',e12.3,' to ',e12.3/
2 13x,'Periodic boundary conditions'/
2 13x,'Initial data are as follows:'//20x,'t0 = ',e12.5/
2 20x,'tlast = ',e12.5/20x,'n = ',i3//)
c
1200 format(/'Initial profile:',/20(6e12.4/))
c
1500 format(///85('*')///'Run with itol =',i2,' rtol =',e12.2,
1 ' atol =',e12.2,' mf = ',i3//)
c
2000 format(' Output for time t =',e12.5,' current h =',e12.5,
1 ' current order =',i2/20(6e12.4/))
c
3000 format(/'Final statistics for mf = ',i3,': ',
1 i5,' steps,',i6,' res,',i6,' Jacobians,'/
2 20x,' rw size =',i6,', iw size =',i6/
3 20x,i4,' extra res for each jac,',i4,' decomps')
c
4000 format(/'Final time reached for mf = ',i3,
1 ' was t = ',e12.5/25x,'at which istate = ',i2//)
5000 format('Final output is correct to within ',e9.2,
1 ' times local error tolerance.'/)
5001 format('Final output is wrong by ',e9.2,
1 ' times local error tolerance.'/)
6000 format(///85('*')//
1 'Run completed: number of errors encountered =',i3)
c
c end of main program for the SLSODIS demonstration program
end
subroutine struct(ia, ja, ic, jc, n)
c This subroutine computes the initial sparse data structure of
c the mass (ia,ja) and Jacobian (ic,jc) matrices.
c
integer ia(*), ja(*), ic(*), jc(*), n, jj, k, l, m
c
write(6,1200)
k = 0
do 33 l = 1,n
ia(l) = (l-1)*3+1
ic(l) = (l-1)*3+1
do 32 m = l,l+2
k = k + 1
ja(k) = m - 1
jc(k) = m - 1
32 continue
33 continue
ia(n+1) = 3*n + 1
ic(n+1) = 3*n+1
ja(1) = n
jc(1) = n
ja(k) = 1
jc(k) = 1
c
write(6,1300) (ia(jj),jj=1,n+1)
write(6,1350) (ja(jj),jj=1,k)
write(6,1400) (ic(jj),jj=1,n+1)
write(6,1450) (jc(jj),jj=1,k)
return
1200 format('Initial sparse data structures'/)
1300 format(' ia ',15i4/10(5x,15i4/))
1350 format(' ja ',15i4/10(5x,15i4/))
1400 format(' ic ',15i4/10(5x,15i4/))
1450 format(' jc ',15i4/10(5x,15i4/))
end
subroutine res (n, t, y, v, r, ires)
c This subroutine computes the residual vector
c r = g(t,y) - A(t,y)*v .
c If ires = -1, only g(t,y) is returned in r, since A(t,y) does
c not depend on y.
c No changes need to be made to this routine if n is changed.
c
integer n, ires, i
real t, y(n), v(n), r(n), r4d, eodsq, one, four, six,
1 fact1, fact4
common /test1/ r4d, eodsq
data one /1.0e0/, four /4.0e0/, six /6.0e0/
c
call gfun (n, t, y, r)
if (ires .eq. -1) return
c
fact1 = one/six
fact4 = four/six
c
r(1) = r(1) - (fact4*v(1) + fact1*(v(2) + v(n)))
do 10 i = 2,n-1
r(i) = r(i) - (fact4*v(i) + fact1*(v(i-1) + v(i+1)))
10 continue
r(n) = r(n) - (fact4*v(n) + fact1*(v(1) + v(n-1)))
return
c end of subroutine res for the SLSODIS demonstration program
end
subroutine gfun (n, t, y, g)
c This subroutine computes the right-hand side function g(y,t).
c It uses r4d = 1/(4*delta) and eodsq = eta/delta**2
c from the Common block test1.
c
integer n, i
real t, y(n), g(n), r4d, eodsq, two
common /test1/ r4d, eodsq
data two/2.0e0/
c
g(1) = r4d*(y(n)**2 - y(2)**2) + eodsq*(y(2) - two*y(1) + y(n))
c
do 20 i = 2,n-1
g(i) = r4d*(y(i-1)**2 - y(i+1)**2)
1 + eodsq*(y(i+1) - two*y(i) + y(i-1))
20 continue
c
g(n) = r4d*(y(n-1)**2 - y(1)**2) + eodsq*(y(1)-two*y(n)+y(n-1))
c
return
c end of subroutine gfun for the SLSODIS demonstration program
end
subroutine addasp (n, t, y, j, ip, jp, pa)
c This subroutine computes the sparse matrix A by columns, adds it to
c pa, and returns the sum in pa.
c The matrix A is periodic tridiagonal, of order n, with nonzero elements
c (reading across) of 1/6, 4/6, 1/6, with 1/6 in the lower left and
c upper right corners.
c
integer n, j, ip(*), jp(*), jm1, jp1
real t, y(n), pa(n), fact1, fact4, one, four, six
data one/1.0e0/, four/4.0e0/, six/6.0e0/
c
c Compute the elements of A.
fact1 = one/six
fact4 = four/six
jm1 = j - 1
jp1 = j + 1
if (j .eq. n) jp1 = 1
if (j .eq. 1) jm1 = n
c
c Add the matrix A to the matrix pa (sparse).
pa(j) = pa(j) + fact4
pa(jp1) = pa(jp1) + fact1
pa(jm1) = pa(jm1) + fact1
return
c end of subroutine addasp for the SLSODIS demonstration program
end
subroutine jacsp (n, t, y, s, j, ip, jp, pdj)
c This subroutine computes the Jacobian dg/dy = d(g-A*s)/dy by
c columns in sparse matrix format. Only nonzeros are loaded.
c It uses r4d = 1/(4*delta) and eodsq = eta/delta**2 from the Common
c block test1.
c
integer n, j, ip(*), jp(*), jm1, jp1
real t, y(n), s(n), pdj(n), r4d, eodsq, two, diag, r2d
common /test1/ r4d, eodsq
data two/2.0e0/
c
diag = -two*eodsq
r2d = two*r4d
jm1 = j - 1
jp1 = j + 1
if (j .eq. 1) jm1 = n
if (j .eq. n) jp1 = 1
c
pdj(jm1) = -r2d*y(j) + eodsq
pdj(j) = diag
pdj(jp1) = r2d*y(j) + eodsq
return
c end of subroutine jacsp for the SLSODIS demonstration program
end
real function elkup (n, y, ewt, itol, rtol,atol, lout)
c This routine looks up approximately correct values of y at t = 0.4,
c ytrue = y12 or y120 depending on whether n = 12 or 120.
c These were obtained by running with very tight tolerances.
c The returned value is
c elkup = norm of [ (y - ytrue) / (rtol*abs(ytrue) + atol) ].
c
integer n, itol, lout, i
real y(n), ewt(n), rtol, atol, y12(12), y120(120),
1 y120a(16), y120b(16), y120c(16), y120d(16), y120e(16),
2 y120f(16), y120g(16), y120h(8), svnorm
equivalence (y120a(1),y120(1)), (y120b(1),y120(17)),
1 (y120c(1),y120(33)), (y120d(1),y120(49)),
1 (y120e(1),y120(65)),
1 (y120f(1),y120(81)), (y120g(1),y120(97)),
1 (y120h(1),y120(113))
data y12/
1 1.60581860e-02, 3.23063251e-02, 1.21903380e-01, 2.70943828e-01,
1 4.60951522e-01, 6.57571216e-01, 8.25154453e-01, 9.35644796e-01,
1 9.90167557e-01, 9.22421221e-01, 5.85764902e-01, 1.81112615e-01/
data y120a /
1 1.89009068e-02, 1.63261891e-02, 1.47080563e-02, 1.39263623e-02,
1 1.38901341e-02, 1.45336989e-02, 1.58129308e-02, 1.77017162e-02,
1 2.01886844e-02, 2.32742221e-02, 2.69677715e-02, 3.12854037e-02,
1 3.62476563e-02, 4.18776225e-02, 4.81992825e-02, 5.52360652e-02/
data y120b /
1 6.30096338e-02, 7.15388849e-02, 8.08391507e-02, 9.09215944e-02,
1 1.01792784e-01, 1.13454431e-01, 1.25903273e-01, 1.39131085e-01,
1 1.53124799e-01, 1.67866712e-01, 1.83334757e-01, 1.99502830e-01,
1 2.16341144e-01, 2.33816600e-01, 2.51893167e-01, 2.70532241e-01/
data y120c /
1 2.89693007e-01, 3.09332757e-01, 3.29407198e-01, 3.49870723e-01,
1 3.70676646e-01, 3.91777421e-01, 4.13124817e-01, 4.34670077e-01,
1 4.56364053e-01, 4.78157319e-01, 5.00000270e-01, 5.21843218e-01,
1 5.43636473e-01, 5.65330432e-01, 5.86875670e-01, 6.08223037e-01/
data y120d /
1 6.29323777e-01, 6.50129662e-01, 6.70593142e-01, 6.90667536e-01,
1 7.10307235e-01, 7.29467947e-01, 7.48106966e-01, 7.66183477e-01,
1 7.83658878e-01, 8.00497138e-01, 8.16665158e-01, 8.32133153e-01,
1 8.46875019e-01, 8.60868691e-01, 8.74096465e-01, 8.86545273e-01/
data y120e /
1 8.98206892e-01, 9.09078060e-01, 9.19160487e-01, 9.28460742e-01,
1 9.36989986e-01, 9.44763554e-01, 9.51800339e-01, 9.58122004e-01,
1 9.63751979e-01, 9.68714242e-01, 9.73031887e-01, 9.76725449e-01,
1 9.79811001e-01, 9.82297985e-01, 9.84186787e-01, 9.85466039e-01/
data y120f /
1 9.86109629e-01, 9.86073433e-01, 9.85291781e-01, 9.83673704e-01,
1 9.81099057e-01, 9.77414704e-01, 9.72431015e-01, 9.65919133e-01,
1 9.57609585e-01, 9.47193093e-01, 9.34324619e-01, 9.18631922e-01,
1 8.99729965e-01, 8.77242371e-01, 8.50830623e-01, 8.20230644e-01/
data y120g /
1 7.85294781e-01, 7.46035145e-01, 7.02662039e-01, 6.55609682e-01,
1 6.05541326e-01, 5.53327950e-01, 4.99999118e-01, 4.46670394e-01,
1 3.94457322e-01, 3.44389410e-01, 2.97337561e-01, 2.53964948e-01,
1 2.14705729e-01, 1.79770169e-01, 1.49170367e-01, 1.22758681e-01/
data y120h /
1 1.00271052e-01, 8.13689920e-02, 6.56761515e-02, 5.28075160e-02,
1 4.23908624e-02, 3.40811650e-02, 2.75691506e-02, 2.25853507e-02/
c
if ((n-12)*(n-120) .ne. 0) go to 300
if (n .eq. 120) go to 100
c
c Compute local error tolerance using correct y (n = 12).
call sewset(n, itol, rtol, atol, y12, ewt)
c
c Invert ewt and replace y by the error, y - ytrue.
do 20 i = 1, 12
ewt(i) = 1.0e0/ewt(i)
20 y(i) = y(i) - y12(i)
go to 200
c
c Compute local error tolerance using correct y (n = 120).
100 call sewset( n, itol, rtol, atol, y120, ewt )
c
c Invert ewt and replace y by the error, y - ytrue.
do 120 i = 1, 120
ewt(i) = 1.0e0/ewt(i)
120 y(i) = y(i) - y120(i)
c
c Find weighted norm of the error.
200 elkup = svnorm (n, y, ewt)
return
c
c error return
300 write(lout,400) n
elkup = 1.0e3
400 format(/5x,'Illegal use of elkup for n =',i4)
return
c end of function elkup for the SLSODIS demonstration program
end
................................................................................
Demonstration Program for DLSODIS
-- Simplified Galerkin solution of Burgers equation --
Diffusion coefficient is eta = 0.50E-01
Uniform mesh on interval -0.100E+01 to 0.100E+01
Periodic boundary conditions
Initial data are as follows:
t0 = 0.00000E+00
tlast = 0.40000E+00
n = 12
Initial profile:
0.0000E+00 0.0000E+00 0.0000E+00 0.5000E+00 0.1000E+01 0.1000E+01
0.1000E+01 0.1000E+01 0.1000E+01 0.5000E+00 0.0000E+00 0.0000E+00
Initial sparse data structures
ia 1 4 7 10 13 16 19 22 25 28 31 34 37
ja 12 1 2 1 2 3 2 3 4 3 4 5 4 5 6
5 6 7 6 7 8 7 8 9 8 9 10 9 10 11
10 11 12 11 12 1
ic 1 4 7 10 13 16 19 22 25 28 31 34 37
jc 12 1 2 1 2 3 2 3 4 3 4 5 4 5 6
5 6 7 6 7 8 7 8 9 8 9 10 9 10 11
10 11 12 11 12 1
*************************************************************************************
Run with itol = 1 rtol = 0.10E-02 atol = 0.10E-02 mf = 11
Output for time t = 0.10000E+00 current h = 0.49176E-01 current order = 2
-0.1463E-02 -0.3833E-02 0.7844E-01 0.3812E+00 0.7671E+00 0.9728E+00
0.1005E+01 0.1001E+01 0.9973E+00 0.6591E+00 0.1534E+00 -0.9859E-02
Output for time t = 0.20000E+00 current h = 0.49176E-01 current order = 2
-0.8416E-02 0.1100E-01 0.1057E+00 0.3273E+00 0.6182E+00 0.8599E+00
0.9783E+00 0.1002E+01 0.1002E+01 0.7756E+00 0.3045E+00 0.2427E-01
Output for time t = 0.30000E+00 current h = 0.82814E-01 current order = 2
-0.3693E-02 0.2323E-01 0.1173E+00 0.2941E+00 0.5236E+00 0.7478E+00
0.9094E+00 0.9830E+00 0.1004E+01 0.8622E+00 0.4498E+00 0.8959E-01
Output for time t = 0.40000E+00 current h = 0.82814E-01 current order = 2
0.1620E-01 0.3267E-01 0.1222E+00 0.2704E+00 0.4595E+00 0.6569E+00
0.8269E+00 0.9378E+00 0.9903E+00 0.9215E+00 0.5849E+00 0.1806E+00
Final statistics for mf = 11: 10 steps, 14 res, 4 Jacobians,
rw size = 421, iw size = 128
0 extra res for each jac, 4 decomps
Final output is correct to within 0.60E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-02 atol = 0.10E-02 mf = 12
Output for time t = 0.10000E+00 current h = 0.49176E-01 current order = 2
-0.1463E-02 -0.3833E-02 0.7844E-01 0.3812E+00 0.7671E+00 0.9728E+00
0.1005E+01 0.1001E+01 0.9973E+00 0.6591E+00 0.1534E+00 -0.9859E-02
Output for time t = 0.20000E+00 current h = 0.49176E-01 current order = 2
-0.8416E-02 0.1100E-01 0.1057E+00 0.3273E+00 0.6182E+00 0.8599E+00
0.9783E+00 0.1002E+01 0.1002E+01 0.7756E+00 0.3045E+00 0.2427E-01
Output for time t = 0.30000E+00 current h = 0.82814E-01 current order = 2
-0.3693E-02 0.2323E-01 0.1173E+00 0.2941E+00 0.5236E+00 0.7478E+00
0.9094E+00 0.9830E+00 0.1004E+01 0.8622E+00 0.4498E+00 0.8959E-01
Output for time t = 0.40000E+00 current h = 0.82814E-01 current order = 2
0.1620E-01 0.3267E-01 0.1222E+00 0.2704E+00 0.4595E+00 0.6569E+00
0.8269E+00 0.9378E+00 0.9903E+00 0.9215E+00 0.5849E+00 0.1806E+00
Final statistics for mf = 12: 10 steps, 30 res, 4 Jacobians,
rw size = 429, iw size = 128
3 extra res for each jac, 4 decomps
Final output is correct to within 0.60E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-02 atol = 0.10E-02 mf = 21
Output for time t = 0.10000E+00 current h = 0.41065E-01 current order = 3
-0.1679E-02 -0.3550E-02 0.7815E-01 0.3816E+00 0.7669E+00 0.9726E+00
0.1006E+01 0.1000E+01 0.9974E+00 0.6590E+00 0.1534E+00 -0.9738E-02
Output for time t = 0.20000E+00 current h = 0.41065E-01 current order = 3
-0.9106E-02 0.1195E-01 0.1044E+00 0.3292E+00 0.6187E+00 0.8565E+00
0.9795E+00 0.1002E+01 0.1002E+01 0.7752E+00 0.3044E+00 0.2472E-01
Output for time t = 0.30000E+00 current h = 0.41065E-01 current order = 3
-0.3840E-02 0.2325E-01 0.1168E+00 0.2953E+00 0.5256E+00 0.7457E+00
0.9071E+00 0.9838E+00 0.1004E+01 0.8621E+00 0.4499E+00 0.8988E-01
Output for time t = 0.40000E+00 current h = 0.67572E-01 current order = 3
0.1612E-01 0.3233E-01 0.1218E+00 0.2713E+00 0.4617E+00 0.6568E+00
0.8235E+00 0.9363E+00 0.9915E+00 0.9222E+00 0.5853E+00 0.1811E+00
Final statistics for mf = 21: 13 steps, 18 res, 4 Jacobians,
rw size = 337, iw size = 128
0 extra res for each jac, 4 decomps
Final output is correct to within 0.41E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-02 atol = 0.10E-02 mf = 22
Output for time t = 0.10000E+00 current h = 0.41065E-01 current order = 3
-0.1679E-02 -0.3550E-02 0.7815E-01 0.3816E+00 0.7669E+00 0.9726E+00
0.1006E+01 0.1000E+01 0.9974E+00 0.6590E+00 0.1534E+00 -0.9738E-02
Output for time t = 0.20000E+00 current h = 0.41065E-01 current order = 3
-0.9106E-02 0.1195E-01 0.1044E+00 0.3292E+00 0.6187E+00 0.8565E+00
0.9795E+00 0.1002E+01 0.1002E+01 0.7752E+00 0.3044E+00 0.2472E-01
Output for time t = 0.30000E+00 current h = 0.41065E-01 current order = 3
-0.3840E-02 0.2325E-01 0.1168E+00 0.2953E+00 0.5256E+00 0.7457E+00
0.9071E+00 0.9838E+00 0.1004E+01 0.8621E+00 0.4499E+00 0.8988E-01
Output for time t = 0.40000E+00 current h = 0.67572E-01 current order = 3
0.1612E-01 0.3233E-01 0.1218E+00 0.2713E+00 0.4617E+00 0.6568E+00
0.8235E+00 0.9363E+00 0.9915E+00 0.9222E+00 0.5853E+00 0.1811E+00
Final statistics for mf = 22: 13 steps, 34 res, 4 Jacobians,
rw size = 345, iw size = 128
3 extra res for each jac, 4 decomps
Final output is correct to within 0.41E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-02 atol = 0.10E-02 mf = 111
Output for time t = 0.10000E+00 current h = 0.49176E-01 current order = 2
-0.1463E-02 -0.3833E-02 0.7844E-01 0.3812E+00 0.7671E+00 0.9728E+00
0.1005E+01 0.1001E+01 0.9973E+00 0.6591E+00 0.1534E+00 -0.9859E-02
Output for time t = 0.20000E+00 current h = 0.49176E-01 current order = 2
-0.8416E-02 0.1100E-01 0.1057E+00 0.3273E+00 0.6182E+00 0.8599E+00
0.9783E+00 0.1002E+01 0.1002E+01 0.7756E+00 0.3045E+00 0.2427E-01
Output for time t = 0.30000E+00 current h = 0.82814E-01 current order = 2
-0.3693E-02 0.2323E-01 0.1173E+00 0.2941E+00 0.5236E+00 0.7478E+00
0.9094E+00 0.9830E+00 0.1004E+01 0.8622E+00 0.4498E+00 0.8959E-01
Output for time t = 0.40000E+00 current h = 0.82814E-01 current order = 2
0.1620E-01 0.3267E-01 0.1222E+00 0.2704E+00 0.4595E+00 0.6569E+00
0.8269E+00 0.9378E+00 0.9903E+00 0.9215E+00 0.5849E+00 0.1806E+00
Final statistics for mf = 111: 10 steps, 14 res, 4 Jacobians,
rw size = 421, iw size = 30
0 extra res for each jac, 4 decomps
Final output is correct to within 0.60E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-02 atol = 0.10E-02 mf = 112
Output for time t = 0.10000E+00 current h = 0.49176E-01 current order = 2
-0.1463E-02 -0.3833E-02 0.7844E-01 0.3812E+00 0.7671E+00 0.9728E+00
0.1005E+01 0.1001E+01 0.9973E+00 0.6591E+00 0.1534E+00 -0.9859E-02
Output for time t = 0.20000E+00 current h = 0.49176E-01 current order = 2
-0.8416E-02 0.1100E-01 0.1057E+00 0.3273E+00 0.6182E+00 0.8599E+00
0.9783E+00 0.1002E+01 0.1002E+01 0.7756E+00 0.3045E+00 0.2427E-01
Output for time t = 0.30000E+00 current h = 0.82814E-01 current order = 2
-0.3693E-02 0.2323E-01 0.1173E+00 0.2941E+00 0.5236E+00 0.7478E+00
0.9094E+00 0.9830E+00 0.1004E+01 0.8622E+00 0.4498E+00 0.8959E-01
Output for time t = 0.40000E+00 current h = 0.82814E-01 current order = 2
0.1620E-01 0.3267E-01 0.1222E+00 0.2704E+00 0.4595E+00 0.6569E+00
0.8269E+00 0.9378E+00 0.9903E+00 0.9215E+00 0.5849E+00 0.1806E+00
Final statistics for mf = 112: 10 steps, 30 res, 4 Jacobians,
rw size = 429, iw size = 30
3 extra res for each jac, 4 decomps
Final output is correct to within 0.60E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-02 atol = 0.10E-02 mf = 121
Output for time t = 0.10000E+00 current h = 0.41065E-01 current order = 3
-0.1679E-02 -0.3550E-02 0.7815E-01 0.3816E+00 0.7669E+00 0.9726E+00
0.1006E+01 0.1000E+01 0.9974E+00 0.6590E+00 0.1534E+00 -0.9738E-02
Output for time t = 0.20000E+00 current h = 0.41065E-01 current order = 3
-0.9106E-02 0.1195E-01 0.1044E+00 0.3292E+00 0.6187E+00 0.8565E+00
0.9795E+00 0.1002E+01 0.1002E+01 0.7752E+00 0.3044E+00 0.2472E-01
Output for time t = 0.30000E+00 current h = 0.41065E-01 current order = 3
-0.3840E-02 0.2325E-01 0.1168E+00 0.2953E+00 0.5256E+00 0.7457E+00
0.9071E+00 0.9838E+00 0.1004E+01 0.8621E+00 0.4499E+00 0.8988E-01
Output for time t = 0.40000E+00 current h = 0.67572E-01 current order = 3
0.1612E-01 0.3233E-01 0.1218E+00 0.2713E+00 0.4617E+00 0.6568E+00
0.8235E+00 0.9363E+00 0.9915E+00 0.9222E+00 0.5853E+00 0.1811E+00
Final statistics for mf = 121: 13 steps, 18 res, 4 Jacobians,
rw size = 337, iw size = 30
0 extra res for each jac, 4 decomps
Final output is correct to within 0.41E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-02 atol = 0.10E-02 mf = 122
Output for time t = 0.10000E+00 current h = 0.41065E-01 current order = 3
-0.1679E-02 -0.3550E-02 0.7815E-01 0.3816E+00 0.7669E+00 0.9726E+00
0.1006E+01 0.1000E+01 0.9974E+00 0.6590E+00 0.1534E+00 -0.9738E-02
Output for time t = 0.20000E+00 current h = 0.41065E-01 current order = 3
-0.9106E-02 0.1195E-01 0.1044E+00 0.3292E+00 0.6187E+00 0.8565E+00
0.9795E+00 0.1002E+01 0.1002E+01 0.7752E+00 0.3044E+00 0.2472E-01
Output for time t = 0.30000E+00 current h = 0.41065E-01 current order = 3
-0.3840E-02 0.2325E-01 0.1168E+00 0.2953E+00 0.5256E+00 0.7457E+00
0.9071E+00 0.9838E+00 0.1004E+01 0.8621E+00 0.4499E+00 0.8988E-01
Output for time t = 0.40000E+00 current h = 0.67572E-01 current order = 3
0.1612E-01 0.3233E-01 0.1218E+00 0.2713E+00 0.4617E+00 0.6568E+00
0.8235E+00 0.9363E+00 0.9915E+00 0.9222E+00 0.5853E+00 0.1811E+00
Final statistics for mf = 122: 13 steps, 34 res, 4 Jacobians,
rw size = 345, iw size = 30
3 extra res for each jac, 4 decomps
Final output is correct to within 0.41E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-02 atol = 0.10E-02 mf = 211
Output for time t = 0.10000E+00 current h = 0.49176E-01 current order = 2
-0.1463E-02 -0.3833E-02 0.7844E-01 0.3812E+00 0.7671E+00 0.9728E+00
0.1005E+01 0.1001E+01 0.9973E+00 0.6591E+00 0.1534E+00 -0.9859E-02
Output for time t = 0.20000E+00 current h = 0.49176E-01 current order = 2
-0.8416E-02 0.1100E-01 0.1057E+00 0.3273E+00 0.6182E+00 0.8599E+00
0.9783E+00 0.1002E+01 0.1002E+01 0.7756E+00 0.3045E+00 0.2427E-01
Output for time t = 0.30000E+00 current h = 0.82814E-01 current order = 2
-0.3693E-02 0.2323E-01 0.1173E+00 0.2941E+00 0.5236E+00 0.7478E+00
0.9094E+00 0.9830E+00 0.1004E+01 0.8622E+00 0.4498E+00 0.8959E-01
Output for time t = 0.40000E+00 current h = 0.82814E-01 current order = 2
0.1620E-01 0.3267E-01 0.1222E+00 0.2704E+00 0.4595E+00 0.6569E+00
0.8269E+00 0.9378E+00 0.9903E+00 0.9215E+00 0.5849E+00 0.1806E+00
Final statistics for mf = 211: 10 steps, 14 res, 4 Jacobians,
rw size = 421, iw size = 30
0 extra res for each jac, 4 decomps
Final output is correct to within 0.60E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-02 atol = 0.10E-02 mf = 212
Output for time t = 0.10000E+00 current h = 0.49176E-01 current order = 2
-0.1463E-02 -0.3833E-02 0.7844E-01 0.3812E+00 0.7671E+00 0.9728E+00
0.1005E+01 0.1001E+01 0.9973E+00 0.6591E+00 0.1534E+00 -0.9859E-02
Output for time t = 0.20000E+00 current h = 0.49176E-01 current order = 2
-0.8416E-02 0.1100E-01 0.1057E+00 0.3273E+00 0.6182E+00 0.8599E+00
0.9783E+00 0.1002E+01 0.1002E+01 0.7756E+00 0.3045E+00 0.2427E-01
Output for time t = 0.30000E+00 current h = 0.82814E-01 current order = 2
-0.3693E-02 0.2323E-01 0.1173E+00 0.2941E+00 0.5236E+00 0.7478E+00
0.9094E+00 0.9830E+00 0.1004E+01 0.8622E+00 0.4498E+00 0.8959E-01
Output for time t = 0.40000E+00 current h = 0.82814E-01 current order = 2
0.1620E-01 0.3267E-01 0.1222E+00 0.2704E+00 0.4595E+00 0.6569E+00
0.8269E+00 0.9378E+00 0.9903E+00 0.9215E+00 0.5849E+00 0.1806E+00
Final statistics for mf = 212: 10 steps, 30 res, 4 Jacobians,
rw size = 429, iw size = 30
3 extra res for each jac, 4 decomps
Final output is correct to within 0.60E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-02 atol = 0.10E-02 mf = 221
Output for time t = 0.10000E+00 current h = 0.41065E-01 current order = 3
-0.1679E-02 -0.3550E-02 0.7815E-01 0.3816E+00 0.7669E+00 0.9726E+00
0.1006E+01 0.1000E+01 0.9974E+00 0.6590E+00 0.1534E+00 -0.9738E-02
Output for time t = 0.20000E+00 current h = 0.41065E-01 current order = 3
-0.9106E-02 0.1195E-01 0.1044E+00 0.3292E+00 0.6187E+00 0.8565E+00
0.9795E+00 0.1002E+01 0.1002E+01 0.7752E+00 0.3044E+00 0.2472E-01
Output for time t = 0.30000E+00 current h = 0.41065E-01 current order = 3
-0.3840E-02 0.2325E-01 0.1168E+00 0.2953E+00 0.5256E+00 0.7457E+00
0.9071E+00 0.9838E+00 0.1004E+01 0.8621E+00 0.4499E+00 0.8988E-01
Output for time t = 0.40000E+00 current h = 0.67572E-01 current order = 3
0.1612E-01 0.3233E-01 0.1218E+00 0.2713E+00 0.4617E+00 0.6568E+00
0.8235E+00 0.9363E+00 0.9915E+00 0.9222E+00 0.5853E+00 0.1811E+00
Final statistics for mf = 221: 13 steps, 18 res, 4 Jacobians,
rw size = 337, iw size = 30
0 extra res for each jac, 4 decomps
Final output is correct to within 0.41E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-02 atol = 0.10E-02 mf = 222
Output for time t = 0.10000E+00 current h = 0.41065E-01 current order = 3
-0.1679E-02 -0.3550E-02 0.7815E-01 0.3816E+00 0.7669E+00 0.9726E+00
0.1006E+01 0.1000E+01 0.9974E+00 0.6590E+00 0.1534E+00 -0.9738E-02
Output for time t = 0.20000E+00 current h = 0.41065E-01 current order = 3
-0.9106E-02 0.1195E-01 0.1044E+00 0.3292E+00 0.6187E+00 0.8565E+00
0.9795E+00 0.1002E+01 0.1002E+01 0.7752E+00 0.3044E+00 0.2472E-01
Output for time t = 0.30000E+00 current h = 0.41065E-01 current order = 3
-0.3840E-02 0.2325E-01 0.1168E+00 0.2953E+00 0.5256E+00 0.7457E+00
0.9071E+00 0.9838E+00 0.1004E+01 0.8621E+00 0.4499E+00 0.8988E-01
Output for time t = 0.40000E+00 current h = 0.67572E-01 current order = 3
0.1612E-01 0.3233E-01 0.1218E+00 0.2713E+00 0.4617E+00 0.6568E+00
0.8235E+00 0.9363E+00 0.9915E+00 0.9222E+00 0.5853E+00 0.1811E+00
Final statistics for mf = 222: 13 steps, 34 res, 4 Jacobians,
rw size = 345, iw size = 30
3 extra res for each jac, 4 decomps
Final output is correct to within 0.41E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-02 atol = 0.10E-02 mf = 311
Output for time t = 0.10000E+00 current h = 0.49176E-01 current order = 2
-0.1463E-02 -0.3833E-02 0.7844E-01 0.3812E+00 0.7671E+00 0.9728E+00
0.1005E+01 0.1001E+01 0.9973E+00 0.6591E+00 0.1534E+00 -0.9859E-02
Output for time t = 0.20000E+00 current h = 0.49176E-01 current order = 2
-0.8416E-02 0.1100E-01 0.1057E+00 0.3273E+00 0.6182E+00 0.8599E+00
0.9783E+00 0.1002E+01 0.1002E+01 0.7756E+00 0.3045E+00 0.2427E-01
Output for time t = 0.30000E+00 current h = 0.82814E-01 current order = 2
-0.3693E-02 0.2323E-01 0.1173E+00 0.2941E+00 0.5236E+00 0.7478E+00
0.9094E+00 0.9830E+00 0.1004E+01 0.8622E+00 0.4498E+00 0.8959E-01
Output for time t = 0.40000E+00 current h = 0.82814E-01 current order = 2
0.1620E-01 0.3267E-01 0.1222E+00 0.2704E+00 0.4595E+00 0.6569E+00
0.8269E+00 0.9378E+00 0.9903E+00 0.9215E+00 0.5849E+00 0.1806E+00
Final statistics for mf = 311: 10 steps, 14 res, 4 Jacobians,
rw size = 421, iw size = 79
0 extra res for each jac, 4 decomps
Final output is correct to within 0.60E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-02 atol = 0.10E-02 mf = 312
Output for time t = 0.10000E+00 current h = 0.49176E-01 current order = 2
-0.1463E-02 -0.3833E-02 0.7844E-01 0.3812E+00 0.7671E+00 0.9728E+00
0.1005E+01 0.1001E+01 0.9973E+00 0.6591E+00 0.1534E+00 -0.9859E-02
Output for time t = 0.20000E+00 current h = 0.49176E-01 current order = 2
-0.8416E-02 0.1100E-01 0.1057E+00 0.3273E+00 0.6182E+00 0.8599E+00
0.9783E+00 0.1002E+01 0.1002E+01 0.7756E+00 0.3045E+00 0.2427E-01
Output for time t = 0.30000E+00 current h = 0.82814E-01 current order = 2
-0.3693E-02 0.2323E-01 0.1173E+00 0.2941E+00 0.5236E+00 0.7478E+00
0.9094E+00 0.9830E+00 0.1004E+01 0.8622E+00 0.4498E+00 0.8959E-01
Output for time t = 0.40000E+00 current h = 0.82814E-01 current order = 2
0.1620E-01 0.3267E-01 0.1222E+00 0.2704E+00 0.4595E+00 0.6569E+00
0.8269E+00 0.9378E+00 0.9903E+00 0.9215E+00 0.5849E+00 0.1806E+00
Final statistics for mf = 312: 10 steps, 30 res, 4 Jacobians,
rw size = 429, iw size = 79
3 extra res for each jac, 4 decomps
Final output is correct to within 0.60E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-02 atol = 0.10E-02 mf = 321
Output for time t = 0.10000E+00 current h = 0.41065E-01 current order = 3
-0.1679E-02 -0.3550E-02 0.7815E-01 0.3816E+00 0.7669E+00 0.9726E+00
0.1006E+01 0.1000E+01 0.9974E+00 0.6590E+00 0.1534E+00 -0.9738E-02
Output for time t = 0.20000E+00 current h = 0.41065E-01 current order = 3
-0.9106E-02 0.1195E-01 0.1044E+00 0.3292E+00 0.6187E+00 0.8565E+00
0.9795E+00 0.1002E+01 0.1002E+01 0.7752E+00 0.3044E+00 0.2472E-01
Output for time t = 0.30000E+00 current h = 0.41065E-01 current order = 3
-0.3840E-02 0.2325E-01 0.1168E+00 0.2953E+00 0.5256E+00 0.7457E+00
0.9071E+00 0.9838E+00 0.1004E+01 0.8621E+00 0.4499E+00 0.8988E-01
Output for time t = 0.40000E+00 current h = 0.67572E-01 current order = 3
0.1612E-01 0.3233E-01 0.1218E+00 0.2713E+00 0.4617E+00 0.6568E+00
0.8235E+00 0.9363E+00 0.9915E+00 0.9222E+00 0.5853E+00 0.1811E+00
Final statistics for mf = 321: 13 steps, 18 res, 4 Jacobians,
rw size = 337, iw size = 79
0 extra res for each jac, 4 decomps
Final output is correct to within 0.41E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-02 atol = 0.10E-02 mf = 322
Output for time t = 0.10000E+00 current h = 0.41065E-01 current order = 3
-0.1679E-02 -0.3550E-02 0.7815E-01 0.3816E+00 0.7669E+00 0.9726E+00
0.1006E+01 0.1000E+01 0.9974E+00 0.6590E+00 0.1534E+00 -0.9738E-02
Output for time t = 0.20000E+00 current h = 0.41065E-01 current order = 3
-0.9106E-02 0.1195E-01 0.1044E+00 0.3292E+00 0.6187E+00 0.8565E+00
0.9795E+00 0.1002E+01 0.1002E+01 0.7752E+00 0.3044E+00 0.2472E-01
Output for time t = 0.30000E+00 current h = 0.41065E-01 current order = 3
-0.3840E-02 0.2325E-01 0.1168E+00 0.2953E+00 0.5256E+00 0.7457E+00
0.9071E+00 0.9838E+00 0.1004E+01 0.8621E+00 0.4499E+00 0.8988E-01
Output for time t = 0.40000E+00 current h = 0.67572E-01 current order = 3
0.1612E-01 0.3233E-01 0.1218E+00 0.2713E+00 0.4617E+00 0.6568E+00
0.8235E+00 0.9363E+00 0.9915E+00 0.9222E+00 0.5853E+00 0.1811E+00
Final statistics for mf = 322: 13 steps, 34 res, 4 Jacobians,
rw size = 345, iw size = 79
3 extra res for each jac, 4 decomps
Final output is correct to within 0.41E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-02 atol = 0.10E-02 mf = 411
Output for time t = 0.10000E+00 current h = 0.49176E-01 current order = 2
-0.1463E-02 -0.3833E-02 0.7844E-01 0.3812E+00 0.7671E+00 0.9728E+00
0.1005E+01 0.1001E+01 0.9973E+00 0.6591E+00 0.1534E+00 -0.9859E-02
Output for time t = 0.20000E+00 current h = 0.49176E-01 current order = 2
-0.8416E-02 0.1100E-01 0.1057E+00 0.3273E+00 0.6182E+00 0.8599E+00
0.9783E+00 0.1002E+01 0.1002E+01 0.7756E+00 0.3045E+00 0.2427E-01
Output for time t = 0.30000E+00 current h = 0.82814E-01 current order = 2
-0.3693E-02 0.2323E-01 0.1173E+00 0.2941E+00 0.5236E+00 0.7478E+00
0.9094E+00 0.9830E+00 0.1004E+01 0.8622E+00 0.4498E+00 0.8959E-01
Output for time t = 0.40000E+00 current h = 0.82814E-01 current order = 2
0.1620E-01 0.3267E-01 0.1222E+00 0.2704E+00 0.4595E+00 0.6569E+00
0.8269E+00 0.9378E+00 0.9903E+00 0.9215E+00 0.5849E+00 0.1806E+00
Final statistics for mf = 411: 10 steps, 14 res, 4 Jacobians,
rw size = 421, iw size = 79
0 extra res for each jac, 4 decomps
Final output is correct to within 0.60E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-02 atol = 0.10E-02 mf = 412
Output for time t = 0.10000E+00 current h = 0.49176E-01 current order = 2
-0.1463E-02 -0.3833E-02 0.7844E-01 0.3812E+00 0.7671E+00 0.9728E+00
0.1005E+01 0.1001E+01 0.9973E+00 0.6591E+00 0.1534E+00 -0.9859E-02
Output for time t = 0.20000E+00 current h = 0.49176E-01 current order = 2
-0.8416E-02 0.1100E-01 0.1057E+00 0.3273E+00 0.6182E+00 0.8599E+00
0.9783E+00 0.1002E+01 0.1002E+01 0.7756E+00 0.3045E+00 0.2427E-01
Output for time t = 0.30000E+00 current h = 0.82814E-01 current order = 2
-0.3693E-02 0.2323E-01 0.1173E+00 0.2941E+00 0.5236E+00 0.7478E+00
0.9094E+00 0.9830E+00 0.1004E+01 0.8622E+00 0.4498E+00 0.8959E-01
Output for time t = 0.40000E+00 current h = 0.82814E-01 current order = 2
0.1620E-01 0.3267E-01 0.1222E+00 0.2704E+00 0.4595E+00 0.6569E+00
0.8269E+00 0.9378E+00 0.9903E+00 0.9215E+00 0.5849E+00 0.1806E+00
Final statistics for mf = 412: 10 steps, 30 res, 4 Jacobians,
rw size = 429, iw size = 79
3 extra res for each jac, 4 decomps
Final output is correct to within 0.60E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-02 atol = 0.10E-02 mf = 421
Output for time t = 0.10000E+00 current h = 0.41065E-01 current order = 3
-0.1679E-02 -0.3550E-02 0.7815E-01 0.3816E+00 0.7669E+00 0.9726E+00
0.1006E+01 0.1000E+01 0.9974E+00 0.6590E+00 0.1534E+00 -0.9738E-02
Output for time t = 0.20000E+00 current h = 0.41065E-01 current order = 3
-0.9106E-02 0.1195E-01 0.1044E+00 0.3292E+00 0.6187E+00 0.8565E+00
0.9795E+00 0.1002E+01 0.1002E+01 0.7752E+00 0.3044E+00 0.2472E-01
Output for time t = 0.30000E+00 current h = 0.41065E-01 current order = 3
-0.3840E-02 0.2325E-01 0.1168E+00 0.2953E+00 0.5256E+00 0.7457E+00
0.9071E+00 0.9838E+00 0.1004E+01 0.8621E+00 0.4499E+00 0.8988E-01
Output for time t = 0.40000E+00 current h = 0.67572E-01 current order = 3
0.1612E-01 0.3233E-01 0.1218E+00 0.2713E+00 0.4617E+00 0.6568E+00
0.8235E+00 0.9363E+00 0.9915E+00 0.9222E+00 0.5853E+00 0.1811E+00
Final statistics for mf = 421: 13 steps, 18 res, 4 Jacobians,
rw size = 337, iw size = 79
0 extra res for each jac, 4 decomps
Final output is correct to within 0.41E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-02 atol = 0.10E-02 mf = 422
Output for time t = 0.10000E+00 current h = 0.41065E-01 current order = 3
-0.1679E-02 -0.3550E-02 0.7815E-01 0.3816E+00 0.7669E+00 0.9726E+00
0.1006E+01 0.1000E+01 0.9974E+00 0.6590E+00 0.1534E+00 -0.9738E-02
Output for time t = 0.20000E+00 current h = 0.41065E-01 current order = 3
-0.9106E-02 0.1195E-01 0.1044E+00 0.3292E+00 0.6187E+00 0.8565E+00
0.9795E+00 0.1002E+01 0.1002E+01 0.7752E+00 0.3044E+00 0.2472E-01
Output for time t = 0.30000E+00 current h = 0.41065E-01 current order = 3
-0.3840E-02 0.2325E-01 0.1168E+00 0.2953E+00 0.5256E+00 0.7457E+00
0.9071E+00 0.9838E+00 0.1004E+01 0.8621E+00 0.4499E+00 0.8988E-01
Output for time t = 0.40000E+00 current h = 0.67572E-01 current order = 3
0.1612E-01 0.3233E-01 0.1218E+00 0.2713E+00 0.4617E+00 0.6568E+00
0.8235E+00 0.9363E+00 0.9915E+00 0.9222E+00 0.5853E+00 0.1811E+00
Final statistics for mf = 422: 13 steps, 34 res, 4 Jacobians,
rw size = 345, iw size = 79
3 extra res for each jac, 4 decomps
Final output is correct to within 0.41E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-05 atol = 0.10E-05 mf = 11
Output for time t = 0.10000E+00 current h = 0.17717E-01 current order = 5
-0.1666E-02 -0.3562E-02 0.7808E-01 0.3817E+00 0.7672E+00 0.9718E+00
0.1006E+01 0.1001E+01 0.9973E+00 0.6590E+00 0.1534E+00 -0.9756E-02
Output for time t = 0.20000E+00 current h = 0.17717E-01 current order = 5
-0.8514E-02 0.1107E-01 0.1054E+00 0.3279E+00 0.6190E+00 0.8586E+00
0.9773E+00 0.1003E+01 0.1002E+01 0.7754E+00 0.3045E+00 0.2439E-01
Output for time t = 0.30000E+00 current h = 0.24980E-01 current order = 5
-0.3772E-02 0.2305E-01 0.1171E+00 0.2947E+00 0.5251E+00 0.7475E+00
0.9073E+00 0.9823E+00 0.1004E+01 0.8626E+00 0.4499E+00 0.8982E-01
Output for time t = 0.40000E+00 current h = 0.34040E-01 current order = 5
0.1606E-01 0.3231E-01 0.1219E+00 0.2709E+00 0.4610E+00 0.6576E+00
0.8252E+00 0.9356E+00 0.9902E+00 0.9224E+00 0.5858E+00 0.1811E+00
Final statistics for mf = 11: 28 steps, 38 res, 7 Jacobians,
rw size = 421, iw size = 128
0 extra res for each jac, 7 decomps
Final output is correct to within 0.41E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-05 atol = 0.10E-05 mf = 12
Output for time t = 0.10000E+00 current h = 0.17717E-01 current order = 5
-0.1666E-02 -0.3562E-02 0.7808E-01 0.3817E+00 0.7672E+00 0.9718E+00
0.1006E+01 0.1001E+01 0.9973E+00 0.6590E+00 0.1534E+00 -0.9756E-02
Output for time t = 0.20000E+00 current h = 0.17717E-01 current order = 5
-0.8514E-02 0.1107E-01 0.1054E+00 0.3279E+00 0.6190E+00 0.8586E+00
0.9773E+00 0.1003E+01 0.1002E+01 0.7754E+00 0.3045E+00 0.2439E-01
Output for time t = 0.30000E+00 current h = 0.24980E-01 current order = 5
-0.3772E-02 0.2305E-01 0.1171E+00 0.2947E+00 0.5251E+00 0.7475E+00
0.9073E+00 0.9823E+00 0.1004E+01 0.8626E+00 0.4499E+00 0.8982E-01
Output for time t = 0.40000E+00 current h = 0.34040E-01 current order = 5
0.1606E-01 0.3231E-01 0.1219E+00 0.2709E+00 0.4610E+00 0.6576E+00
0.8252E+00 0.9356E+00 0.9902E+00 0.9224E+00 0.5858E+00 0.1811E+00
Final statistics for mf = 12: 28 steps, 66 res, 7 Jacobians,
rw size = 429, iw size = 128
3 extra res for each jac, 7 decomps
Final output is correct to within 0.41E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-05 atol = 0.10E-05 mf = 21
Output for time t = 0.10000E+00 current h = 0.91135E-02 current order = 4
-0.1666E-02 -0.3563E-02 0.7808E-01 0.3817E+00 0.7672E+00 0.9718E+00
0.1006E+01 0.1001E+01 0.9973E+00 0.6590E+00 0.1534E+00 -0.9756E-02
Output for time t = 0.20000E+00 current h = 0.18660E-01 current order = 5
-0.8514E-02 0.1107E-01 0.1054E+00 0.3279E+00 0.6190E+00 0.8586E+00
0.9773E+00 0.1003E+01 0.1002E+01 0.7754E+00 0.3045E+00 0.2439E-01
Output for time t = 0.30000E+00 current h = 0.18660E-01 current order = 5
-0.3772E-02 0.2305E-01 0.1171E+00 0.2947E+00 0.5251E+00 0.7475E+00
0.9073E+00 0.9823E+00 0.1004E+01 0.8626E+00 0.4499E+00 0.8982E-01
Output for time t = 0.40000E+00 current h = 0.22945E-01 current order = 5
0.1606E-01 0.3231E-01 0.1219E+00 0.2709E+00 0.4610E+00 0.6576E+00
0.8252E+00 0.9356E+00 0.9902E+00 0.9224E+00 0.5858E+00 0.1811E+00
Final statistics for mf = 21: 40 steps, 49 res, 7 Jacobians,
rw size = 337, iw size = 128
0 extra res for each jac, 7 decomps
Final output is correct to within 0.10E+01 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-05 atol = 0.10E-05 mf = 22
Output for time t = 0.10000E+00 current h = 0.91135E-02 current order = 4
-0.1666E-02 -0.3563E-02 0.7808E-01 0.3817E+00 0.7672E+00 0.9718E+00
0.1006E+01 0.1001E+01 0.9973E+00 0.6590E+00 0.1534E+00 -0.9756E-02
Output for time t = 0.20000E+00 current h = 0.18660E-01 current order = 5
-0.8514E-02 0.1107E-01 0.1054E+00 0.3279E+00 0.6190E+00 0.8586E+00
0.9773E+00 0.1003E+01 0.1002E+01 0.7754E+00 0.3045E+00 0.2439E-01
Output for time t = 0.30000E+00 current h = 0.18660E-01 current order = 5
-0.3772E-02 0.2305E-01 0.1171E+00 0.2947E+00 0.5251E+00 0.7475E+00
0.9073E+00 0.9823E+00 0.1004E+01 0.8626E+00 0.4499E+00 0.8982E-01
Output for time t = 0.40000E+00 current h = 0.22945E-01 current order = 5
0.1606E-01 0.3231E-01 0.1219E+00 0.2709E+00 0.4610E+00 0.6576E+00
0.8252E+00 0.9356E+00 0.9902E+00 0.9224E+00 0.5858E+00 0.1811E+00
Final statistics for mf = 22: 40 steps, 77 res, 7 Jacobians,
rw size = 345, iw size = 128
3 extra res for each jac, 7 decomps
Final output is correct to within 0.10E+01 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-05 atol = 0.10E-05 mf = 111
Output for time t = 0.10000E+00 current h = 0.17717E-01 current order = 5
-0.1666E-02 -0.3562E-02 0.7808E-01 0.3817E+00 0.7672E+00 0.9718E+00
0.1006E+01 0.1001E+01 0.9973E+00 0.6590E+00 0.1534E+00 -0.9756E-02
Output for time t = 0.20000E+00 current h = 0.17717E-01 current order = 5
-0.8514E-02 0.1107E-01 0.1054E+00 0.3279E+00 0.6190E+00 0.8586E+00
0.9773E+00 0.1003E+01 0.1002E+01 0.7754E+00 0.3045E+00 0.2439E-01
Output for time t = 0.30000E+00 current h = 0.24980E-01 current order = 5
-0.3772E-02 0.2305E-01 0.1171E+00 0.2947E+00 0.5251E+00 0.7475E+00
0.9073E+00 0.9823E+00 0.1004E+01 0.8626E+00 0.4499E+00 0.8982E-01
Output for time t = 0.40000E+00 current h = 0.34040E-01 current order = 5
0.1606E-01 0.3231E-01 0.1219E+00 0.2709E+00 0.4610E+00 0.6576E+00
0.8252E+00 0.9356E+00 0.9902E+00 0.9224E+00 0.5858E+00 0.1811E+00
Final statistics for mf = 111: 28 steps, 38 res, 7 Jacobians,
rw size = 421, iw size = 30
0 extra res for each jac, 7 decomps
Final output is correct to within 0.41E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-05 atol = 0.10E-05 mf = 112
Output for time t = 0.10000E+00 current h = 0.17717E-01 current order = 5
-0.1666E-02 -0.3562E-02 0.7808E-01 0.3817E+00 0.7672E+00 0.9718E+00
0.1006E+01 0.1001E+01 0.9973E+00 0.6590E+00 0.1534E+00 -0.9756E-02
Output for time t = 0.20000E+00 current h = 0.17717E-01 current order = 5
-0.8514E-02 0.1107E-01 0.1054E+00 0.3279E+00 0.6190E+00 0.8586E+00
0.9773E+00 0.1003E+01 0.1002E+01 0.7754E+00 0.3045E+00 0.2439E-01
Output for time t = 0.30000E+00 current h = 0.24980E-01 current order = 5
-0.3772E-02 0.2305E-01 0.1171E+00 0.2947E+00 0.5251E+00 0.7475E+00
0.9073E+00 0.9823E+00 0.1004E+01 0.8626E+00 0.4499E+00 0.8982E-01
Output for time t = 0.40000E+00 current h = 0.34040E-01 current order = 5
0.1606E-01 0.3231E-01 0.1219E+00 0.2709E+00 0.4610E+00 0.6576E+00
0.8252E+00 0.9356E+00 0.9902E+00 0.9224E+00 0.5858E+00 0.1811E+00
Final statistics for mf = 112: 28 steps, 66 res, 7 Jacobians,
rw size = 429, iw size = 30
3 extra res for each jac, 7 decomps
Final output is correct to within 0.41E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-05 atol = 0.10E-05 mf = 121
Output for time t = 0.10000E+00 current h = 0.91135E-02 current order = 4
-0.1666E-02 -0.3563E-02 0.7808E-01 0.3817E+00 0.7672E+00 0.9718E+00
0.1006E+01 0.1001E+01 0.9973E+00 0.6590E+00 0.1534E+00 -0.9756E-02
Output for time t = 0.20000E+00 current h = 0.18660E-01 current order = 5
-0.8514E-02 0.1107E-01 0.1054E+00 0.3279E+00 0.6190E+00 0.8586E+00
0.9773E+00 0.1003E+01 0.1002E+01 0.7754E+00 0.3045E+00 0.2439E-01
Output for time t = 0.30000E+00 current h = 0.18660E-01 current order = 5
-0.3772E-02 0.2305E-01 0.1171E+00 0.2947E+00 0.5251E+00 0.7475E+00
0.9073E+00 0.9823E+00 0.1004E+01 0.8626E+00 0.4499E+00 0.8982E-01
Output for time t = 0.40000E+00 current h = 0.22945E-01 current order = 5
0.1606E-01 0.3231E-01 0.1219E+00 0.2709E+00 0.4610E+00 0.6576E+00
0.8252E+00 0.9356E+00 0.9902E+00 0.9224E+00 0.5858E+00 0.1811E+00
Final statistics for mf = 121: 40 steps, 49 res, 7 Jacobians,
rw size = 337, iw size = 30
0 extra res for each jac, 7 decomps
Final output is correct to within 0.10E+01 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-05 atol = 0.10E-05 mf = 122
Output for time t = 0.10000E+00 current h = 0.91135E-02 current order = 4
-0.1666E-02 -0.3563E-02 0.7808E-01 0.3817E+00 0.7672E+00 0.9718E+00
0.1006E+01 0.1001E+01 0.9973E+00 0.6590E+00 0.1534E+00 -0.9756E-02
Output for time t = 0.20000E+00 current h = 0.18660E-01 current order = 5
-0.8514E-02 0.1107E-01 0.1054E+00 0.3279E+00 0.6190E+00 0.8586E+00
0.9773E+00 0.1003E+01 0.1002E+01 0.7754E+00 0.3045E+00 0.2439E-01
Output for time t = 0.30000E+00 current h = 0.18660E-01 current order = 5
-0.3772E-02 0.2305E-01 0.1171E+00 0.2947E+00 0.5251E+00 0.7475E+00
0.9073E+00 0.9823E+00 0.1004E+01 0.8626E+00 0.4499E+00 0.8982E-01
Output for time t = 0.40000E+00 current h = 0.22945E-01 current order = 5
0.1606E-01 0.3231E-01 0.1219E+00 0.2709E+00 0.4610E+00 0.6576E+00
0.8252E+00 0.9356E+00 0.9902E+00 0.9224E+00 0.5858E+00 0.1811E+00
Final statistics for mf = 122: 40 steps, 77 res, 7 Jacobians,
rw size = 345, iw size = 30
3 extra res for each jac, 7 decomps
Final output is correct to within 0.10E+01 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-05 atol = 0.10E-05 mf = 211
Output for time t = 0.10000E+00 current h = 0.17717E-01 current order = 5
-0.1666E-02 -0.3562E-02 0.7808E-01 0.3817E+00 0.7672E+00 0.9718E+00
0.1006E+01 0.1001E+01 0.9973E+00 0.6590E+00 0.1534E+00 -0.9756E-02
Output for time t = 0.20000E+00 current h = 0.17717E-01 current order = 5
-0.8514E-02 0.1107E-01 0.1054E+00 0.3279E+00 0.6190E+00 0.8586E+00
0.9773E+00 0.1003E+01 0.1002E+01 0.7754E+00 0.3045E+00 0.2439E-01
Output for time t = 0.30000E+00 current h = 0.24980E-01 current order = 5
-0.3772E-02 0.2305E-01 0.1171E+00 0.2947E+00 0.5251E+00 0.7475E+00
0.9073E+00 0.9823E+00 0.1004E+01 0.8626E+00 0.4499E+00 0.8982E-01
Output for time t = 0.40000E+00 current h = 0.34040E-01 current order = 5
0.1606E-01 0.3231E-01 0.1219E+00 0.2709E+00 0.4610E+00 0.6576E+00
0.8252E+00 0.9356E+00 0.9902E+00 0.9224E+00 0.5858E+00 0.1811E+00
Final statistics for mf = 211: 28 steps, 38 res, 7 Jacobians,
rw size = 421, iw size = 30
0 extra res for each jac, 7 decomps
Final output is correct to within 0.41E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-05 atol = 0.10E-05 mf = 212
Output for time t = 0.10000E+00 current h = 0.17717E-01 current order = 5
-0.1666E-02 -0.3562E-02 0.7808E-01 0.3817E+00 0.7672E+00 0.9718E+00
0.1006E+01 0.1001E+01 0.9973E+00 0.6590E+00 0.1534E+00 -0.9756E-02
Output for time t = 0.20000E+00 current h = 0.17717E-01 current order = 5
-0.8514E-02 0.1107E-01 0.1054E+00 0.3279E+00 0.6190E+00 0.8586E+00
0.9773E+00 0.1003E+01 0.1002E+01 0.7754E+00 0.3045E+00 0.2439E-01
Output for time t = 0.30000E+00 current h = 0.24980E-01 current order = 5
-0.3772E-02 0.2305E-01 0.1171E+00 0.2947E+00 0.5251E+00 0.7475E+00
0.9073E+00 0.9823E+00 0.1004E+01 0.8626E+00 0.4499E+00 0.8982E-01
Output for time t = 0.40000E+00 current h = 0.34040E-01 current order = 5
0.1606E-01 0.3231E-01 0.1219E+00 0.2709E+00 0.4610E+00 0.6576E+00
0.8252E+00 0.9356E+00 0.9902E+00 0.9224E+00 0.5858E+00 0.1811E+00
Final statistics for mf = 212: 28 steps, 66 res, 7 Jacobians,
rw size = 429, iw size = 30
3 extra res for each jac, 7 decomps
Final output is correct to within 0.41E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-05 atol = 0.10E-05 mf = 221
Output for time t = 0.10000E+00 current h = 0.91135E-02 current order = 4
-0.1666E-02 -0.3563E-02 0.7808E-01 0.3817E+00 0.7672E+00 0.9718E+00
0.1006E+01 0.1001E+01 0.9973E+00 0.6590E+00 0.1534E+00 -0.9756E-02
Output for time t = 0.20000E+00 current h = 0.18660E-01 current order = 5
-0.8514E-02 0.1107E-01 0.1054E+00 0.3279E+00 0.6190E+00 0.8586E+00
0.9773E+00 0.1003E+01 0.1002E+01 0.7754E+00 0.3045E+00 0.2439E-01
Output for time t = 0.30000E+00 current h = 0.18660E-01 current order = 5
-0.3772E-02 0.2305E-01 0.1171E+00 0.2947E+00 0.5251E+00 0.7475E+00
0.9073E+00 0.9823E+00 0.1004E+01 0.8626E+00 0.4499E+00 0.8982E-01
Output for time t = 0.40000E+00 current h = 0.22945E-01 current order = 5
0.1606E-01 0.3231E-01 0.1219E+00 0.2709E+00 0.4610E+00 0.6576E+00
0.8252E+00 0.9356E+00 0.9902E+00 0.9224E+00 0.5858E+00 0.1811E+00
Final statistics for mf = 221: 40 steps, 49 res, 7 Jacobians,
rw size = 337, iw size = 30
0 extra res for each jac, 7 decomps
Final output is correct to within 0.10E+01 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-05 atol = 0.10E-05 mf = 222
Output for time t = 0.10000E+00 current h = 0.91135E-02 current order = 4
-0.1666E-02 -0.3563E-02 0.7808E-01 0.3817E+00 0.7672E+00 0.9718E+00
0.1006E+01 0.1001E+01 0.9973E+00 0.6590E+00 0.1534E+00 -0.9756E-02
Output for time t = 0.20000E+00 current h = 0.18660E-01 current order = 5
-0.8514E-02 0.1107E-01 0.1054E+00 0.3279E+00 0.6190E+00 0.8586E+00
0.9773E+00 0.1003E+01 0.1002E+01 0.7754E+00 0.3045E+00 0.2439E-01
Output for time t = 0.30000E+00 current h = 0.18660E-01 current order = 5
-0.3772E-02 0.2305E-01 0.1171E+00 0.2947E+00 0.5251E+00 0.7475E+00
0.9073E+00 0.9823E+00 0.1004E+01 0.8626E+00 0.4499E+00 0.8982E-01
Output for time t = 0.40000E+00 current h = 0.22945E-01 current order = 5
0.1606E-01 0.3231E-01 0.1219E+00 0.2709E+00 0.4610E+00 0.6576E+00
0.8252E+00 0.9356E+00 0.9902E+00 0.9224E+00 0.5858E+00 0.1811E+00
Final statistics for mf = 222: 40 steps, 77 res, 7 Jacobians,
rw size = 345, iw size = 30
3 extra res for each jac, 7 decomps
Final output is correct to within 0.10E+01 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-05 atol = 0.10E-05 mf = 311
Output for time t = 0.10000E+00 current h = 0.17717E-01 current order = 5
-0.1666E-02 -0.3562E-02 0.7808E-01 0.3817E+00 0.7672E+00 0.9718E+00
0.1006E+01 0.1001E+01 0.9973E+00 0.6590E+00 0.1534E+00 -0.9756E-02
Output for time t = 0.20000E+00 current h = 0.17717E-01 current order = 5
-0.8514E-02 0.1107E-01 0.1054E+00 0.3279E+00 0.6190E+00 0.8586E+00
0.9773E+00 0.1003E+01 0.1002E+01 0.7754E+00 0.3045E+00 0.2439E-01
Output for time t = 0.30000E+00 current h = 0.24980E-01 current order = 5
-0.3772E-02 0.2305E-01 0.1171E+00 0.2947E+00 0.5251E+00 0.7475E+00
0.9073E+00 0.9823E+00 0.1004E+01 0.8626E+00 0.4499E+00 0.8982E-01
Output for time t = 0.40000E+00 current h = 0.34040E-01 current order = 5
0.1606E-01 0.3231E-01 0.1219E+00 0.2709E+00 0.4610E+00 0.6576E+00
0.8252E+00 0.9356E+00 0.9902E+00 0.9224E+00 0.5858E+00 0.1811E+00
Final statistics for mf = 311: 28 steps, 38 res, 7 Jacobians,
rw size = 421, iw size = 79
0 extra res for each jac, 7 decomps
Final output is correct to within 0.41E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-05 atol = 0.10E-05 mf = 312
Output for time t = 0.10000E+00 current h = 0.17717E-01 current order = 5
-0.1666E-02 -0.3562E-02 0.7808E-01 0.3817E+00 0.7672E+00 0.9718E+00
0.1006E+01 0.1001E+01 0.9973E+00 0.6590E+00 0.1534E+00 -0.9756E-02
Output for time t = 0.20000E+00 current h = 0.17717E-01 current order = 5
-0.8514E-02 0.1107E-01 0.1054E+00 0.3279E+00 0.6190E+00 0.8586E+00
0.9773E+00 0.1003E+01 0.1002E+01 0.7754E+00 0.3045E+00 0.2439E-01
Output for time t = 0.30000E+00 current h = 0.24980E-01 current order = 5
-0.3772E-02 0.2305E-01 0.1171E+00 0.2947E+00 0.5251E+00 0.7475E+00
0.9073E+00 0.9823E+00 0.1004E+01 0.8626E+00 0.4499E+00 0.8982E-01
Output for time t = 0.40000E+00 current h = 0.34040E-01 current order = 5
0.1606E-01 0.3231E-01 0.1219E+00 0.2709E+00 0.4610E+00 0.6576E+00
0.8252E+00 0.9356E+00 0.9902E+00 0.9224E+00 0.5858E+00 0.1811E+00
Final statistics for mf = 312: 28 steps, 66 res, 7 Jacobians,
rw size = 429, iw size = 79
3 extra res for each jac, 7 decomps
Final output is correct to within 0.41E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-05 atol = 0.10E-05 mf = 321
Output for time t = 0.10000E+00 current h = 0.91135E-02 current order = 4
-0.1666E-02 -0.3563E-02 0.7808E-01 0.3817E+00 0.7672E+00 0.9718E+00
0.1006E+01 0.1001E+01 0.9973E+00 0.6590E+00 0.1534E+00 -0.9756E-02
Output for time t = 0.20000E+00 current h = 0.18660E-01 current order = 5
-0.8514E-02 0.1107E-01 0.1054E+00 0.3279E+00 0.6190E+00 0.8586E+00
0.9773E+00 0.1003E+01 0.1002E+01 0.7754E+00 0.3045E+00 0.2439E-01
Output for time t = 0.30000E+00 current h = 0.18660E-01 current order = 5
-0.3772E-02 0.2305E-01 0.1171E+00 0.2947E+00 0.5251E+00 0.7475E+00
0.9073E+00 0.9823E+00 0.1004E+01 0.8626E+00 0.4499E+00 0.8982E-01
Output for time t = 0.40000E+00 current h = 0.22945E-01 current order = 5
0.1606E-01 0.3231E-01 0.1219E+00 0.2709E+00 0.4610E+00 0.6576E+00
0.8252E+00 0.9356E+00 0.9902E+00 0.9224E+00 0.5858E+00 0.1811E+00
Final statistics for mf = 321: 40 steps, 49 res, 7 Jacobians,
rw size = 337, iw size = 79
0 extra res for each jac, 7 decomps
Final output is correct to within 0.10E+01 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-05 atol = 0.10E-05 mf = 322
Output for time t = 0.10000E+00 current h = 0.91135E-02 current order = 4
-0.1666E-02 -0.3563E-02 0.7808E-01 0.3817E+00 0.7672E+00 0.9718E+00
0.1006E+01 0.1001E+01 0.9973E+00 0.6590E+00 0.1534E+00 -0.9756E-02
Output for time t = 0.20000E+00 current h = 0.18660E-01 current order = 5
-0.8514E-02 0.1107E-01 0.1054E+00 0.3279E+00 0.6190E+00 0.8586E+00
0.9773E+00 0.1003E+01 0.1002E+01 0.7754E+00 0.3045E+00 0.2439E-01
Output for time t = 0.30000E+00 current h = 0.18660E-01 current order = 5
-0.3772E-02 0.2305E-01 0.1171E+00 0.2947E+00 0.5251E+00 0.7475E+00
0.9073E+00 0.9823E+00 0.1004E+01 0.8626E+00 0.4499E+00 0.8982E-01
Output for time t = 0.40000E+00 current h = 0.22945E-01 current order = 5
0.1606E-01 0.3231E-01 0.1219E+00 0.2709E+00 0.4610E+00 0.6576E+00
0.8252E+00 0.9356E+00 0.9902E+00 0.9224E+00 0.5858E+00 0.1811E+00
Final statistics for mf = 322: 40 steps, 77 res, 7 Jacobians,
rw size = 345, iw size = 79
3 extra res for each jac, 7 decomps
Final output is correct to within 0.10E+01 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-05 atol = 0.10E-05 mf = 411
Output for time t = 0.10000E+00 current h = 0.17717E-01 current order = 5
-0.1666E-02 -0.3562E-02 0.7808E-01 0.3817E+00 0.7672E+00 0.9718E+00
0.1006E+01 0.1001E+01 0.9973E+00 0.6590E+00 0.1534E+00 -0.9756E-02
Output for time t = 0.20000E+00 current h = 0.17717E-01 current order = 5
-0.8514E-02 0.1107E-01 0.1054E+00 0.3279E+00 0.6190E+00 0.8586E+00
0.9773E+00 0.1003E+01 0.1002E+01 0.7754E+00 0.3045E+00 0.2439E-01
Output for time t = 0.30000E+00 current h = 0.24980E-01 current order = 5
-0.3772E-02 0.2305E-01 0.1171E+00 0.2947E+00 0.5251E+00 0.7475E+00
0.9073E+00 0.9823E+00 0.1004E+01 0.8626E+00 0.4499E+00 0.8982E-01
Output for time t = 0.40000E+00 current h = 0.34040E-01 current order = 5
0.1606E-01 0.3231E-01 0.1219E+00 0.2709E+00 0.4610E+00 0.6576E+00
0.8252E+00 0.9356E+00 0.9902E+00 0.9224E+00 0.5858E+00 0.1811E+00
Final statistics for mf = 411: 28 steps, 38 res, 7 Jacobians,
rw size = 421, iw size = 79
0 extra res for each jac, 7 decomps
Final output is correct to within 0.41E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-05 atol = 0.10E-05 mf = 412
Output for time t = 0.10000E+00 current h = 0.17717E-01 current order = 5
-0.1666E-02 -0.3562E-02 0.7808E-01 0.3817E+00 0.7672E+00 0.9718E+00
0.1006E+01 0.1001E+01 0.9973E+00 0.6590E+00 0.1534E+00 -0.9756E-02
Output for time t = 0.20000E+00 current h = 0.17717E-01 current order = 5
-0.8514E-02 0.1107E-01 0.1054E+00 0.3279E+00 0.6190E+00 0.8586E+00
0.9773E+00 0.1003E+01 0.1002E+01 0.7754E+00 0.3045E+00 0.2439E-01
Output for time t = 0.30000E+00 current h = 0.24980E-01 current order = 5
-0.3772E-02 0.2305E-01 0.1171E+00 0.2947E+00 0.5251E+00 0.7475E+00
0.9073E+00 0.9823E+00 0.1004E+01 0.8626E+00 0.4499E+00 0.8982E-01
Output for time t = 0.40000E+00 current h = 0.34040E-01 current order = 5
0.1606E-01 0.3231E-01 0.1219E+00 0.2709E+00 0.4610E+00 0.6576E+00
0.8252E+00 0.9356E+00 0.9902E+00 0.9224E+00 0.5858E+00 0.1811E+00
Final statistics for mf = 412: 28 steps, 66 res, 7 Jacobians,
rw size = 429, iw size = 79
3 extra res for each jac, 7 decomps
Final output is correct to within 0.41E+00 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-05 atol = 0.10E-05 mf = 421
Output for time t = 0.10000E+00 current h = 0.91135E-02 current order = 4
-0.1666E-02 -0.3563E-02 0.7808E-01 0.3817E+00 0.7672E+00 0.9718E+00
0.1006E+01 0.1001E+01 0.9973E+00 0.6590E+00 0.1534E+00 -0.9756E-02
Output for time t = 0.20000E+00 current h = 0.18660E-01 current order = 5
-0.8514E-02 0.1107E-01 0.1054E+00 0.3279E+00 0.6190E+00 0.8586E+00
0.9773E+00 0.1003E+01 0.1002E+01 0.7754E+00 0.3045E+00 0.2439E-01
Output for time t = 0.30000E+00 current h = 0.18660E-01 current order = 5
-0.3772E-02 0.2305E-01 0.1171E+00 0.2947E+00 0.5251E+00 0.7475E+00
0.9073E+00 0.9823E+00 0.1004E+01 0.8626E+00 0.4499E+00 0.8982E-01
Output for time t = 0.40000E+00 current h = 0.22945E-01 current order = 5
0.1606E-01 0.3231E-01 0.1219E+00 0.2709E+00 0.4610E+00 0.6576E+00
0.8252E+00 0.9356E+00 0.9902E+00 0.9224E+00 0.5858E+00 0.1811E+00
Final statistics for mf = 421: 40 steps, 49 res, 7 Jacobians,
rw size = 337, iw size = 79
0 extra res for each jac, 7 decomps
Final output is correct to within 0.10E+01 times local error tolerance.
*************************************************************************************
Run with itol = 1 rtol = 0.10E-05 atol = 0.10E-05 mf = 422
Output for time t = 0.10000E+00 current h = 0.91135E-02 current order = 4
-0.1666E-02 -0.3563E-02 0.7808E-01 0.3817E+00 0.7672E+00 0.9718E+00
0.1006E+01 0.1001E+01 0.9973E+00 0.6590E+00 0.1534E+00 -0.9756E-02
Output for time t = 0.20000E+00 current h = 0.18660E-01 current order = 5
-0.8514E-02 0.1107E-01 0.1054E+00 0.3279E+00 0.6190E+00 0.8586E+00
0.9773E+00 0.1003E+01 0.1002E+01 0.7754E+00 0.3045E+00 0.2439E-01
Output for time t = 0.30000E+00 current h = 0.18660E-01 current order = 5
-0.3772E-02 0.2305E-01 0.1171E+00 0.2947E+00 0.5251E+00 0.7475E+00
0.9073E+00 0.9823E+00 0.1004E+01 0.8626E+00 0.4499E+00 0.8982E-01
Output for time t = 0.40000E+00 current h = 0.22945E-01 current order = 5
0.1606E-01 0.3231E-01 0.1219E+00 0.2709E+00 0.4610E+00 0.6576E+00
0.8252E+00 0.9356E+00 0.9902E+00 0.9224E+00 0.5858E+00 0.1811E+00
Final statistics for mf = 422: 40 steps, 77 res, 7 Jacobians,
rw size = 345, iw size = 79
3 extra res for each jac, 7 decomps
Final output is correct to within 0.10E+01 times local error tolerance.
*************************************************************************************
Run completed: number of errors encountered = 0