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Fundamental TechnologiesVoyager LECP Pages |
by Sheela Shodhan
******************************************************************* * THIS PROGRAM IS THE DIFFERENTIAL EQUATION SOLVER-DHPCG WHICH * * USES THE HAMMING'S MODIFIED FOURTH ORDER PREDICTOR-CORRECTOR * * DOUBLE-PRECISION METHOD. * * THIS IS A MODIFICATION OF SUBROUTINE DHPCG FROM THE * * SCIENTIFIC SUBROUTINE PACKAGE (SSP) PUBLISHED BY * * IBM. THE ORIGINAL VERSION OF THE ROUTINE WAS WRITTEN IN * * FORTRAN-4 WITH NO INDENTATION AS WELL AS POORLY * * STRUCTURED. * * THE FOLLOWING VERSION IS VERY MUCH MODERNIZED TO A STRUCTURED * * CODE AND INDENTED IN FORTRAN-77. THE USERS ARE REFERED TO THE * * MANUAL OF SSP FOR FURTHER IMFORMATION ABOUT THE METHODS AND * * DETAILED DESCRIPTION. * *******************************************************************
SUBROUTINE DHPCG(PRMT,PV,DERY,NDIM,IHLF,FCT,OUTP,AUX)
REAL*8 PRMT(1),X,H,Z,DELT,PV(1),DERY(1),AUX(16,1)
INTEGER NHIT
COMMON /NHIT/NHIT
NHIT=0
N=1
IHLF1=0
IHLF=0
X=PRMT(1)
H=PRMT(3)
PRMT(5)=0.D0
DO I=1,NDIM
AUX(16,I)=0.D0
AUX(15,I)=DERY(I)
AUX(1,I)=PV(I)
END DO
C ERROR RETURNS
IF((H*PRMT(2)).LT.X*H) THEN
IHLF=13
ELSE IF((H*PRMT(2)).EQ.X*H) THEN
IHLF=12
END IF
ISW=0
C ****************************************************************
C
C COMPUTATION OF DERY FOR STARTING VALUES
C BLOCK 1 VS OLD LABELS 4_20
C
C ***************************************************************
DO WHILE (ISW.NE.4)
IF(ISW.EQ.0) THEN
IHLF1=0
CALL FCT(X,PV,DERY)
C RECORDING OF STARTING VALUES
CALL OUTP(X,PV,DERY,IHLF,NDIM,PRMT,NHIT)
IF (NHIT.NE.0) RETURN
IF(PRMT(5).NE.0.) THEN
RETURN
END IF
DO I=1,NDIM
AUX(8,I)=DERY(I)
END DO
C COMPUTATION OF AUX(2,I)
ISW=1
ELSE IF(ISW.EQ.1) THEN
IF(IHLF1.NE.1) THEN
X=X+H
DO I=1,NDIM
AUX(2,I)=PV(I)
END DO
END IF
IHLF1=0
C INCREMENT IS TESTED BY MEANS OF BISECTION
IHLF=IHLF+1
X=X-H
DO I=1,NDIM
AUX(4,I)=AUX(2,I)
END DO
H=.5D0*H
N=1
ISW=2
ELSE IF(ISW.EQ.2) THEN
X=X+H
CALL FCT(X,PV,DERY)
N=2
DO I=1,NDIM
AUX(2,I)=PV(I)
AUX(9,I)=DERY(I)
ENDDO
ISW=3
ELSE IF(ISW.EQ.3) THEN
C COMPUTATION OF TEST VALUE DELT
DELT=0.D0
DO I=1,NDIM
DELT=DELT+AUX(15,I)*DABS(PV(I)-AUX(4,I))
ENDDO
DELT=.66666666667D-1*DELT
IF(DELE.LE.PRMT(4)) THEN
ISW=5
ELSE
IF(IHLF.GE.10) THEN
IHLF=11
X=X+H
ISW=0
IHLF1=2
ELSE
C NO SATISFACTORY ACCURACY AFTER 10 BISECTIONS. ERROR MESSAGE.
IHLF1=1
ISW=1
ENDIF
ENDIF
ELSE IF(ISW.EQ.5) THEN
C THERE IS SATISFACTORY ACCURACY AFTER LESS THAN 11 BISECTIONS.
X=X+H
CALL FCT(X,PV,DERY)
DO I=1,NDIM
AUX(3,I)=PV(I)
AUX(10,I)=DERY(I)
ENDDO
N=3
ISW=4
ENDIF
C *******************************************************************
C
C THE FOLLOWING PART OF SUBROUTINE HPCG COMPUTES BY MEANS OF
C RUNGE-KUTTA METHOD STARTING VALUES FOR THE NOT SELF-STARTING
C PREDICTOR-CORRECTOR METHOD.
C BLOCK 2 VS OLD LABELS 100_104
C
C *******************************************************************
IF(ISW.NE.5.AND.IHLF1.EQ.0) THEN
DO I=1,NDIM
Z=H*AUX(N+7,I)
AUX(5,I)=Z
PV(I)=AUX(N,I)+.4D0*Z
ENDDO
C Z IS AN AUXILIARY STORAGE LOCATION
Z=X+.4D0*H
CALL FCT(X,PV,DERY)
DO I=1,NDIM
Z=H*DERY(I)
AUX(6,I)=Z
PV(I)=AUX(N,I)+.29697760925D0*AUX(5,I)+.15875964497D0*Z
ENDDO
Z=X+.45573725422D0*H
CALL FCT(X,PV,DERY)
DO I=1,NDIM
Z=H*DERY(I)
AUX(7,I)=Z
PV(I)=AUX(N,I)+0.21810038823D0*AUX(5,I)-3.0509651487D0*AUX(6,I)
* + 3.8328647605D0*Z
ENDDO
Z=X+H
CALL FCT(X,PV,DERY)
DO I=1,NDIM
PV(I)=AUX(N,I)+.17476028223D0*AUX(5,I)-.55148066288D0*AUX(6,I)
* +1.2055355994D0*AUX(7,I)+.17118478122D0*H*DERY(I)
ENDDO
ENDIF
ENDDO
C *******************************************************************
C
C BLOCK 3 VS OLD LABELS 21_22
C
C *******************************************************************
N=1
X=X+H
CALL FCT(X,PV,DERY)
X=PRMT(1)
DO I=1,NDIM
AUX(11,I)=DERY(I)
PV(I)=AUX(1,I)+H*(.375D0*AUX(8,I)+.79166666667D0*AUX(9,I)
* -.20833333333D0*AUX(10,I)+.41666666667D-1*DERY(I))
ENDDO
C *********************************************************************
C
C BLOCK 4 VS OLD LABELS 23_30
C
C *********************************************************************
DO WHILE (N.LT.4)
X=X+H
N=N+1
CALL FCT(X,PV,DERY)
CALL OUTP(X,PV,DERY,IHLF,NDIM,PRMT,NHIT)
IF (NHIT.NE.0) RETURN
IF(PRMT(5).NE.0) THEN
RETURN
ELSE IF((N-4).LT.0) THEN
DO I=1,NDIM
AUX(N,I)=PV(I)
AUX(N+7,I)=DERY(I)
ENDDO
IF(N.LT.3) THEN
DO I=1,NDIM
DELT=AUX(9,I)+AUX(9,I)
DELT=DELT+DELT
PV(I)=AUX(1,I)+.33333333333D0*H*(AUX(8,I)+DELT+AUX(10,I))
ENDDO
ELSE
DO I=1,NDIM
DELT=AUX(9,I)+AUX(10,I)
DELT=DELT+DELT+DELT
PV(I)=AUX(1,I)+.375D0*H*(AUX(8,I)+DELT+AUX(11,I))
ENDDO
ENDIF
ENDIF
ENDDO
ISW=6
C ******************************************************************
C
C POSSIBLE BREAK POINT FOR LINKAGE
C STARTING VALUES ARE COMPUTED
C NOW START HAMMINGS MODIFIED PREDICTOR-CORRECTOR METHOD.
C BLOCK 5 VS OLD LABELS 200_226
C
C ******************************************************************
ISTEP=3
DO WHILE (ISW.GE.6)
IF(ISW.EQ.6) THEN
IF(N.EQ.8) THEN
C N=8 CAUSES THE ROWS OF AUX TO CHANGE THEIR STORAGE LOCATIONS
DO N=2,7
DO I=1,NDIM
AUX(N-1,I)=AUX(N,I)
AUX(N+6,I)=AUX(N+7,I)
ENDDO
ENDDO
N=7
ENDIF
C N LESS THAN 8 CAUSES N+1 TO GET N
N=N+1
C COMPUTATION OF NEXT VECTOR PV
DO I=1,NDIM
AUX(N-1,I)=PV(I)
AUX(N+6,I)=DERY(I)
ENDDO
X=X+H
ISW=7
ELSE IF(ISW.EQ.7) THEN
ISTEP=ISTEP+1
DO I=1,NDIM
DELT=AUX(N-4,I)+1.3333333333D0*H*(AUX(N+6,I)+AUX(N+6,I)
* -AUX(N+5,I)+AUX(N+4,I)+AUX(N+4,I))
PV(I)=DELT-.92561983471D0*AUX(16,I)
AUX(16,I)=DELT
ENDDO
C PREDICTOR IS NOW GENERATED IN ROW 16 OF AUX, MODIFIED PREDICTOR
C IS GENERATED I PV. DELT MEANS AN AUXILIARY STORAGE.
CALL FCT(X,PV,DERY)
C DERIVATIVE OF MODIFIED PREDICTOR IS GENERATED IN DERY
DO I=1,NDIM
DELT=.125D0*(9.D0*AUX(N-1,I)-AUX(N-3,I)+3.D0*H*(DERY(I)
* +AUX(N+6,I)+AUX(N+6,I)-AUX(N+5,I)))
AUX(16,I)=AUX(16,I)-DELT
PV(I)=DELT+.7438016529D-1*AUX(16,I)
ENDDO
C TEST WHETHER H MUST BE HALVED OR DOUBLED
DELT=0.D0
DO I=1,NDIM
DELT=DELT+AUX(15,I)*DABS(AUX(16,I))
ENDDO
ISW=8
ELSE IF(ISW.EQ.8) THEN
IF(DELT.LT.PRMT(4).OR.IHLF1.EQ.5) THEN
IHLF1=0
C H MUST NOT BE HALVED. THAT MEANS PV(I) ARE GOOD.
CALL FCT(X,PV,DERY)
CALL OUTP(X,PV,DERY,IHLF,NDIM,PRMT,NHIT)
IF (NHIT.NE.0) RETURN
IF(PRMT(5).NE.0.OR.IHLF.GE.11.OR.(H*(X-PRMT(2))).GE.0
* .OR.DABS(X-PRMT(2)).LT.0.1D0*DABS(H)) THEN
1150 FORMAT(I5)
RETURN
ELSE
IF(DELT.LE..2D-1*PRMT(4).AND.IHLF.GT.0.AND.N.GE.7.AND.
* ISTEP.GE.4) THEN
C H COULD BE DOUBLED IF ALL NECESSARY PRECEEDING VALUES ARE AVAILABLE
IMOD=ISTEP/2
IF((ISTEP-IMOD-IMOD).EQ.0) THEN
H=H+H
IHLF=IHLF-1
ISTEP=0
DO I=1,NDIM
AUX(N-1,I)=AUX(N-2,I)
AUX(N-2,I)=AUX(N-4,I)
AUX(N-3,I)=AUX(N-6,I)
AUX(N+6,I)=AUX(N+5,I)
AUX(N+5,I)=AUX(N+3,I)
AUX(N+4,I)=AUX(N+1,I)
DELT=AUX(N+6,I)+AUX(N+5,I)
DELT=DELT+DELT+DELT
AUX(16,I)=8.962962963D0*(PV(I)-AUX(N-3,I))-3.361111111D0*H*
* (DERY(I)+DELT+AUX(N+4,I))
ENDDO
ISW=6
ELSE
ISW=6
ENDIF
ELSE
ISW=6
ENDIF
ENDIF
ISW=6
ELSE
ISW=9
ENDIF
ELSE IF(ISW.EQ.9) THEN
C H MUST BE HALVED
IHLF=IHLF+1
IF(IHLF.LE.10) THEN
ISW=10
ELSE
ISW=8
IHLF1=5
ENDIF
ELSE IF(ISW.EQ.10) THEN
H=.5D0*H
ISTEP=0
DO I=1,NDIM
PV(I)=.390625D-2*(8.D1*AUX(N-1,I)+135.D0*AUX(N-2,I)
* + 4.D1*AUX(N-1,I)+AUX(N-4,I))-.1171875D0*(AUX(N+6,I)
* - 6.D0*AUX(N+5,I)-AUX(N+4,I))*H
AUX(N-4,I)=.390625D-2*(12.D0*AUX(N-1,I)+135.D0*AUX(N-2,I)+
* 08.D0*AUX(N-3,I)+AUX(N-4,I))-.234375D-1*(AUX(N+6,I)+
* 8.D0*AUX(N+5,I)-9.D0*AUX(N+4,I))*H
AUX(N-3,I)=AUX(N-2,I)
AUX(N+4,I)=AUX(N+5,I)
ENDDO
X=X-H
DELT=X-(H+H)
CALL FCT(X,PV,DERY)
DO I=1,NDIM
AUX(N-2,I)=PV(I)
AUX(N+5,I)=DERY(I)
PV(I)=AUX(N-4,I)
ENDDO
DELT=DELT-(H+H)
CALL FCT(X,PV,DERY)
DO I=1,NDIM
DELT=AUX(N+5,I)+AUX(N+4,I)
DELT=DELT+DELT+DELT
AUX(16,I)=8.9629696296D0*(AUX(N-1,I)-PV(I))
* - 3.3611111111D0*H*(AUX(N+6,I)+DELT+DERY(I))
AUX(N+3,I)=DERY(I)
ENDDO
ISW=7
ENDIF
ENDDO
END
C-----------------------------------------------------------------------
C-----------------------------------------------------------------------
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Last modified 12/9/02, Tizby Hunt-Ward
tizby@ftecs.com