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*DECK EVORK
SUBROUTINE EVORK(Y,N,X,HTRY,EPS,YSCAL,HDID,HNEXT,MU1,IMA,MAXA,
1 NSUPF,NFISS,KFISS,YSF,ADPL,BDPL)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Fifth-order Runge-Kutta Cash-Karp step with monitoring of local
* truncation error to ensure accuracy and adjust stepsize.
* Special version for isotopic depletion calculations.
*
*Copyright:
* Copyright (C) 2002 Ecole Polytechnique de Montreal
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version
*
*Author(s): A. Hebert
*
*Parameters: input/output
* Y dependent variable vector.
* N size of the dependent variable vector.
* X independent variable.
* HTRY stepsize to be attempted.
* EPS required accuracy.
* YSCAL vector against which the error is scaled.
* HDID stepsize that was actually accomplished.
* HNEXT estimated next stepsize.
* MU1 position of each diagonal element in vectors ADPL and ASS.
* IMA position of the first non-zero column element in vectors
* ADPL and ASS.
* MAXA first dimension of matrix ADPL.
* NSUPF number of depleting fission products.
* NFISS number of fissile isotopes producing fission products.
* KFISS position in chain of the fissile isotopes.
* YSF components of the product of the fission yields and fission
* rates.
* ADPL depletion matrix components.
* BDPL depletion source components.
*
*Reference:
* W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery,
* "Numerical recipes in Fortran, Second edition, Chapter 16,
* Cambridge, 1992.
*
*-----------------------------------------------------------------------
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER N,MU1(N),IMA(N),MAXA,NSUPF,NFISS,KFISS(NFISS)
REAL Y(N),X,HTRY,EPS,YSCAL(N),HDID,HNEXT,YSF(NFISS,NSUPF,2),
1 ADPL(MAXA,2),BDPL(N,2)
*----
* LOCAL VARIABLES
*----
PARAMETER (A2=.2,A3=.3,A4=.6,A5=1.,A6=.875,B21=.2,B31=3./40.,
*B32=9./40.,B41=.3,B42=-.9,B43=1.2,B51=-11./54.,B52=2.5,
*B53=-70./27.,B54=35./27.,B61=1631./55296.,B62=175./512.,
*B63=575./13824.,B64=44275./110592.,B65=253./4096.,C1=37./378.,
*C3=250./621.,C4=125./594.,C6=512./1771.,DC1=C1-2825./27648.,
*DC3=C3-18575./48384.,DC4=C4-13525./55296.,DC5=-277./14336.,
*DC6=C6-.25)
PARAMETER (SAFETY=0.85,PGROW=-.2,PSHRNK=-.25,GROW=1.5,SHRNK=0.5)
CHARACTER HSMG*131
REAL, ALLOCATABLE, DIMENSION(:) :: YTEMP,YGAR
REAL, ALLOCATABLE, DIMENSION(:,:) :: AK
*----
* SCRATCH STORAGE ALLOCATION
*----
ALLOCATE(YTEMP(N),YGAR(N),AK(N,6))
*
NSUPL=N-NSUPF
H=HTRY
10 CALL ALLUM(N,ADPL(1,1),Y(1),AK(1,1),MU1,IMA,1)
CALL ALLUM(N,ADPL(1,2),Y(1),YGAR(1),MU1,IMA,1)
DO 25 I=1,NSUPF
DO 20 J=1,NFISS
AK(NSUPL+I,1)=AK(NSUPL+I,1)+YSF(J,I,1)*Y(KFISS(J))
YGAR(NSUPL+I)=YGAR(NSUPL+I)+YSF(J,I,2)*Y(KFISS(J))
20 CONTINUE
25 CONTINUE
DO 30 I=1,N
AK(I,1)=AK(I,1)+BDPL(I,1)+X*(YGAR(I)+BDPL(I,2))
YTEMP(I)=Y(I)+H*B21*AK(I,1)
30 CONTINUE
*
CALL ALLUM(N,ADPL(1,1),YTEMP(1),AK(1,2),MU1,IMA,1)
CALL ALLUM(N,ADPL(1,2),YTEMP(1),YGAR(1),MU1,IMA,1)
DO 45 I=1,NSUPF
DO 40 J=1,NFISS
AK(NSUPL+I,2)=AK(NSUPL+I,2)+YSF(J,I,1)*YTEMP(KFISS(J))
YGAR(NSUPL+I)=YGAR(NSUPL+I)+YSF(J,I,2)*YTEMP(KFISS(J))
40 CONTINUE
45 CONTINUE
DO 50 I=1,N
AK(I,2)=AK(I,2)+BDPL(I,1)+(X+A2*H)*(YGAR(I)+BDPL(I,2))
YTEMP(I)=Y(I)+H*(B31*AK(I,1)+B32*AK(I,2))
50 CONTINUE
*
CALL ALLUM(N,ADPL(1,1),YTEMP(1),AK(1,3),MU1,IMA,1)
CALL ALLUM(N,ADPL(1,2),YTEMP(1),YGAR(1),MU1,IMA,1)
DO 65 I=1,NSUPF
DO 60 J=1,NFISS
AK(NSUPL+I,3)=AK(NSUPL+I,3)+YSF(J,I,1)*YTEMP(KFISS(J))
YGAR(NSUPL+I)=YGAR(NSUPL+I)+YSF(J,I,2)*YTEMP(KFISS(J))
60 CONTINUE
65 CONTINUE
DO 70 I=1,N
AK(I,3)=AK(I,3)+BDPL(I,1)+(X+A3*H)*(YGAR(I)+BDPL(I,2))
YTEMP(I)=Y(I)+H*(B41*AK(I,1)+B42*AK(I,2)+B43*AK(I,3))
70 CONTINUE
*
CALL ALLUM(N,ADPL(1,1),YTEMP(1),AK(1,4),MU1,IMA,1)
CALL ALLUM(N,ADPL(1,2),YTEMP(1),YGAR(1),MU1,IMA,1)
DO 85 I=1,NSUPF
DO 80 J=1,NFISS
AK(NSUPL+I,4)=AK(NSUPL+I,4)+YSF(J,I,1)*YTEMP(KFISS(J))
YGAR(NSUPL+I)=YGAR(NSUPL+I)+YSF(J,I,2)*YTEMP(KFISS(J))
80 CONTINUE
85 CONTINUE
DO 90 I=1,N
AK(I,4)=AK(I,4)+BDPL(I,1)+(X+A4*H)*(YGAR(I)+BDPL(I,2))
YTEMP(I)=Y(I)+H*(B51*AK(I,1)+B52*AK(I,2)+B53*AK(I,3)+B54*AK(I,4))
90 CONTINUE
*
CALL ALLUM(N,ADPL(1,1),YTEMP(1),AK(1,5),MU1,IMA,1)
CALL ALLUM(N,ADPL(1,2),YTEMP(1),YGAR(1),MU1,IMA,1)
DO 105 I=1,NSUPF
DO 100 J=1,NFISS
AK(NSUPL+I,5)=AK(NSUPL+I,5)+YSF(J,I,1)*YTEMP(KFISS(J))
YGAR(NSUPL+I)=YGAR(NSUPL+I)+YSF(J,I,2)*YTEMP(KFISS(J))
100 CONTINUE
105 CONTINUE
DO 110 I=1,N
AK(I,5)=AK(I,5)+BDPL(I,1)+(X+A5*H)*(YGAR(I)+BDPL(I,2))
YTEMP(I)=Y(I)+H*(B61*AK(I,1)+B62*AK(I,2)+B63*AK(I,3)+B64*AK(I,4)+
1 B65*AK(I,5))
110 CONTINUE
*
CALL ALLUM(N,ADPL(1,1),YTEMP(1),AK(1,6),MU1,IMA,1)
CALL ALLUM(N,ADPL(1,2),YTEMP(1),YGAR(1),MU1,IMA,1)
DO 125 I=1,NSUPF
DO 120 J=1,NFISS
AK(NSUPL+I,6)=AK(NSUPL+I,6)+YSF(J,I,1)*YTEMP(KFISS(J))
YGAR(NSUPL+I)=YGAR(NSUPL+I)+YSF(J,I,2)*YTEMP(KFISS(J))
120 CONTINUE
125 CONTINUE
DO 130 I=1,N
AK(I,6)=AK(I,6)+BDPL(I,1)+(X+A6*H)*(YGAR(I)+BDPL(I,2))
YTEMP(I)=Y(I)+H*(C1*AK(I,1)+C3*AK(I,3)+C4*AK(I,4)+C6*AK(I,6))
YGAR(I)=H*(DC1*AK(I,1)+DC3*AK(I,3)+DC4*AK(I,4)+DC5*AK(I,5)+
1 DC6*AK(I,6))
130 CONTINUE
*
ERRMAX=0.0
DO 140 I=1,N
ERRMAX=MAX(ERRMAX,ABS(YGAR(I)/YSCAL(I)))
140 CONTINUE
ERRMAX=ERRMAX/EPS
IF (ERRMAX.EQ.0.0) THEN
HDID=H
HNEXT=GROW*H
X=X+H
DO 150 I=1,N
Y(I)=YTEMP(I)
150 CONTINUE
GO TO 170
ELSE IF (ERRMAX.LE.1.0) THEN
HDID=H
HNEXT=MIN(GROW,SAFETY*(ERRMAX**PGROW))*H
X=X+H
DO 160 I=1,N
Y(I)=YTEMP(I)
160 CONTINUE
GO TO 170
ELSE
H=MAX(SHRNK,SAFETY*(ERRMAX**PSHRNK))*H
XNEW=X+H
IF (X.EQ.XNEW) THEN
WRITE(HSMG,'(35HEVORK: STEPSIZE NOT SIGNIFICANT (H=,1P,E11.4,
1 6H HTRY=,E11.4,2H).)') H,HTRY
CALL XABORT(HSMG)
ENDIF
GO TO 10
ENDIF
*----
* SCRATCH STORAGE DEALLOCATION
*----
170 DEALLOCATE(AK,YGAR,YTEMP)
RETURN
END
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