*DECK CFOD SUBROUTINE CFOD (METH, ELCO, TESCO) C***BEGIN PROLOGUE CFOD C***SUBSIDIARY C***PURPOSE Subsidiary to DEBDF C***LIBRARY SLATEC C***TYPE SINGLE PRECISION (CFOD-S, DCFOD-D) C***AUTHOR (UNKNOWN) C***DESCRIPTION C C CFOD defines coefficients needed in the integrator package DEBDF C C***SEE ALSO DEBDF C***ROUTINES CALLED (NONE) C***REVISION HISTORY (YYMMDD) C 800901 DATE WRITTEN C 890531 Changed all specific intrinsics to generic. (WRB) C 891214 Prologue converted to Version 4.0 format. (BAB) C 900328 Added TYPE section. (WRB) C***END PROLOGUE CFOD C C CLLL. OPTIMIZE INTEGER METH, I, IB, NQ, NQM1, NQP1 REAL ELCO, TESCO, AGAMQ, FNQ, FNQM1, PC, PINT, RAGQ, 1 RQFAC, RQ1FAC, TSIGN, XPIN DIMENSION ELCO(13,12), TESCO(3,12) C----------------------------------------------------------------------- C CFOD IS CALLED BY THE INTEGRATOR ROUTINE TO SET COEFFICIENTS C NEEDED THERE. THE COEFFICIENTS FOR THE CURRENT METHOD, AS C GIVEN BY THE VALUE OF METH, ARE SET FOR ALL ORDERS AND SAVED. C THE MAXIMUM ORDER ASSUMED HERE IS 12 IF METH = 1 AND 5 IF METH = 2. C (A SMALLER VALUE OF THE MAXIMUM ORDER IS ALSO ALLOWED.) C CFOD IS CALLED ONCE AT THE BEGINNING OF THE PROBLEM, C AND IS NOT CALLED AGAIN UNLESS AND UNTIL METH IS CHANGED. C C THE ELCO ARRAY CONTAINS THE BASIC METHOD COEFFICIENTS. C THE COEFFICIENTS EL(I), 1 .LE. I .LE. NQ+1, FOR THE METHOD OF C ORDER NQ ARE STORED IN ELCO(I,NQ). THEY ARE GIVEN BY A GENERATING C POLYNOMIAL, I.E., C L(X) = EL(1) + EL(2)*X + ... + EL(NQ+1)*X**NQ. C FOR THE IMPLICIT ADAMS METHODS, L(X) IS GIVEN BY C DL/DX = (X+1)*(X+2)*...*(X+NQ-1)/FACTORIAL(NQ-1), L(-1) = 0. C FOR THE BDF METHODS, L(X) IS GIVEN BY C L(X) = (X+1)*(X+2)* ... *(X+NQ)/K, C WHERE K = FACTORIAL(NQ)*(1 + 1/2 + ... + 1/NQ). C C THE TESCO ARRAY CONTAINS TEST CONSTANTS USED FOR THE C LOCAL ERROR TEST AND THE SELECTION OF STEP SIZE AND/OR ORDER. C AT ORDER NQ, TESCO(K,NQ) IS USED FOR THE SELECTION OF STEP C SIZE AT ORDER NQ - 1 IF K = 1, AT ORDER NQ IF K = 2, AND AT ORDER C NQ + 1 IF K = 3. C----------------------------------------------------------------------- DIMENSION PC(12) C C***FIRST EXECUTABLE STATEMENT CFOD GO TO (100, 200), METH C 100 ELCO(1,1) = 1.0E0 ELCO(2,1) = 1.0E0 TESCO(1,1) = 0.0E0 TESCO(2,1) = 2.0E0 TESCO(1,2) = 1.0E0 TESCO(3,12) = 0.0E0 PC(1) = 1.0E0 RQFAC = 1.0E0 DO 140 NQ = 2,12 C----------------------------------------------------------------------- C THE PC ARRAY WILL CONTAIN THE COEFFICIENTS OF THE POLYNOMIAL C P(X) = (X+1)*(X+2)*...*(X+NQ-1). C INITIALLY, P(X) = 1. C----------------------------------------------------------------------- RQ1FAC = RQFAC RQFAC = RQFAC/NQ NQM1 = NQ - 1 FNQM1 = NQM1 NQP1 = NQ + 1 C FORM COEFFICIENTS OF P(X)*(X+NQ-1). ---------------------------------- PC(NQ) = 0.0E0 DO 110 IB = 1,NQM1 I = NQP1 - IB 110 PC(I) = PC(I-1) + FNQM1*PC(I) PC(1) = FNQM1*PC(1) C COMPUTE INTEGRAL, -1 TO 0, OF P(X) AND X*P(X). ----------------------- PINT = PC(1) XPIN = PC(1)/2.0E0 TSIGN = 1.0E0 DO 120 I = 2,NQ TSIGN = -TSIGN PINT = PINT + TSIGN*PC(I)/I 120 XPIN = XPIN + TSIGN*PC(I)/(I+1) C STORE COEFFICIENTS IN ELCO AND TESCO. -------------------------------- ELCO(1,NQ) = PINT*RQ1FAC ELCO(2,NQ) = 1.0E0 DO 130 I = 2,NQ 130 ELCO(I+1,NQ) = RQ1FAC*PC(I)/I AGAMQ = RQFAC*XPIN RAGQ = 1.0E0/AGAMQ TESCO(2,NQ) = RAGQ IF(NQ.LT.12)TESCO(1,NQP1)=RAGQ*RQFAC/NQP1 TESCO(3,NQM1) = RAGQ 140 CONTINUE RETURN C 200 PC(1) = 1.0E0 RQ1FAC = 1.0E0 DO 230 NQ = 1,5 C----------------------------------------------------------------------- C THE PC ARRAY WILL CONTAIN THE COEFFICIENTS OF THE POLYNOMIAL C P(X) = (X+1)*(X+2)*...*(X+NQ). C INITIALLY, P(X) = 1. C----------------------------------------------------------------------- FNQ = NQ NQP1 = NQ + 1 C FORM COEFFICIENTS OF P(X)*(X+NQ). ------------------------------------ PC(NQP1) = 0.0E0 DO 210 IB = 1,NQ I = NQ + 2 - IB 210 PC(I) = PC(I-1) + FNQ*PC(I) PC(1) = FNQ*PC(1) C STORE COEFFICIENTS IN ELCO AND TESCO. -------------------------------- DO 220 I = 1,NQP1 220 ELCO(I,NQ) = PC(I)/PC(2) ELCO(2,NQ) = 1.0E0 TESCO(1,NQ) = RQ1FAC TESCO(2,NQ) = NQP1/ELCO(1,NQ) TESCO(3,NQ) = (NQ+2)/ELCO(1,NQ) RQ1FAC = RQ1FAC/FNQ 230 CONTINUE RETURN C----------------------- END OF SUBROUTINE CFOD ----------------------- END