c fishpk26 from portlib 12/30/83 c c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c * * c * f i s h p a k * c * * c * * c * a package of fortran subprograms for the solution of * c * * c * separable elliptic partial differential equations * c * * c * (version 3.1 , october 1980) * c * * c * by * c * * c * john adams, paul swarztrauber and roland sweet * c * * c * of * c * * c * the national center for atmospheric research * c * * c * boulder, colorado (80307) u.s.a. * c * * c * which is sponsored by * c * * c * the national science foundation * c * * c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c c c program to illustrate the use of subroutine hwsplr to solve c the equation c c (1/r)(d/dr)(r*(du/dr)) + (1/r**2)(d/dtheta)(du/dtheta) = 16*r**2 c c on the quarter-disk 0 .lt. r .lt. 1, 0 .lt. theta .lt. pi/2 with c with the boundary conditions c c u(1,theta) = 1 - cos(4*theta), 0 .le. theta .le. 1 c c and c c (du/dtheta)(r,0) = (du/dtheta)(r,pi/2) = 0, 0 .le. r .le. 1. c c (note that the solution u is unspecified at r = 0.) c the r-interval will be divided into 50 panels and the c theta-interval will be divided into 48 panels. c dimension f(100,50) ,bdc(51) ,bdd(51) ,w(1114) , 1 r(51) ,theta(49) c c from dimension statement we get value of idimf. also note that w c is dimensioned 4*(n+1) + (13 + int(log2(n+1)))*(m+1) . c idimf = 100 a = 0. b = 1. m = 50 mbdcnd = 5 c = 0. pi = pimach(dum) d = pi/2. n = 48 nbdcnd = 3 elmbda = 0. c c auxiliary quantities. c mp1 = m+1 np1 = n+1 c c generate and store grid points for the purpose of computing c boundary data and the right side of the poisson equation. c do 101 i=1,mp1 r(i) = float(i-1)/50. 101 continue do 102 j=1,np1 theta(j) = float(j-1)*pi/96. 102 continue c c generate boundary data. c do 103 i=1,mp1 bdc(i) = 0. bdd(i) = 0. 103 continue c c bda and bdb are dummy variables. c do 104 j=1,np1 f(mp1,j) = 1.-cos(4.*theta(j)) 104 continue c c generate right side of equation. c do 106 i=1,m do 105 j=1,np1 f(i,j) = 16.*r(i)**2 105 continue 106 continue call hwsplr (a,b,m,mbdcnd,bda,bdb,c,d,n,nbdcnd,bdc,bdd,elmbda,f, 1 idimf,pertrb,ierror,w) c c compute discretization error. the exact solution is c u(r,theta) = r**4*(1 - cos(4*theta)) c err = 0. do 108 i=1,mp1 do 107 j=1,np1 z = abs(f(i,j)-r(i)**4*(1.-cos(4.*theta(j)))) if (z .gt. err) err = z 107 continue 108 continue print 1001 , ierror,err,w(1) stop c 1001 format (1h1,20x,25hsubroutine hwsplr example/// 1 10x,46hthe output from the ncar control data 7600 was// 2 32x,10hierror = 0/ 3 18x,34hdiscretization error = 6.19134e-04/ 4 12x,32hrequired length of w array = 882// 5 10x,32hthe output from your computer is// 6 32x,8hierror =,i2/18x,22hdiscretization error =,e12.5/ 7 12x,28hrequired length of w array =,f4.0) c end