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73 lines
2.7 KiB
Fortran
73 lines
2.7 KiB
Fortran
*DECK DEFE4
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SUBROUTINE DEFE4 (COFX, IDMN, USOL, GRHS)
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C***BEGIN PROLOGUE DEFE4
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C***SUBSIDIARY
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C***PURPOSE Subsidiary to SEPX4
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C***LIBRARY SLATEC
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C***TYPE SINGLE PRECISION (DEFE4-S)
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C***AUTHOR (UNKNOWN)
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C***DESCRIPTION
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C
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C This subroutine first approximates the truncation error given by
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C TRUN1(X,Y)=DLX**2*TX+DLY**2*TY where
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C TX=AFUN(X)*UXXXX/12.0+BFUN(X)*UXXX/6.0 on the interior and
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C at the boundaries if periodic (here UXXX,UXXXX are the third
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C and fourth partial derivatives of U with respect to X).
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C TX is of the form AFUN(X)/3.0*(UXXXX/4.0+UXXX/DLX)
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C at X=A or X=B if the boundary condition there is mixed.
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C TX=0.0 along specified boundaries. TY has symmetric form
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C in Y with X,AFUN(X),BFUN(X) replaced by Y,DFUN(Y),EFUN(Y).
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C The second order solution in USOL is used to approximate
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C (via second order finite differencing) the truncation error
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C and the result is added to the right hand side in GRHS
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C and then transferred to USOL to be used as a new right
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C hand side when calling BLKTRI for a fourth order solution.
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C
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C***SEE ALSO SEPX4
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C***ROUTINES CALLED DX4, DY4
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C***COMMON BLOCKS SPL4
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C***REVISION HISTORY (YYMMDD)
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C 801001 DATE WRITTEN
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C 890531 Changed all specific intrinsics to generic. (WRB)
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C 900402 Added TYPE section. (WRB)
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C***END PROLOGUE DEFE4
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C
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COMMON /SPL4/ KSWX ,KSWY ,K ,L ,
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1 AIT ,BIT ,CIT ,DIT ,
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2 MIT ,NIT ,IS ,MS ,
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3 JS ,NS ,DLX ,DLY ,
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4 TDLX3 ,TDLY3 ,DLX4 ,DLY4
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DIMENSION GRHS(IDMN,*) ,USOL(IDMN,*)
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EXTERNAL COFX
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C***FIRST EXECUTABLE STATEMENT DEFE4
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DO 30 I=IS,MS
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XI = AIT+(I-1)*DLX
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CALL COFX (XI,AI,BI,CI)
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DO 30 J=JS,NS
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C
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C COMPUTE PARTIAL DERIVATIVE APPROXIMATIONS AT (XI,YJ)
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C
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CALL DX4(USOL,IDMN,I,J,UXXX,UXXXX)
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CALL DY4(USOL,IDMN,I,J,UYYY,UYYYY)
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TX = AI*UXXXX/12.0+BI*UXXX/6.0
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TY=UYYYY/12.0
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C
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C RESET FORM OF TRUNCATION IF AT BOUNDARY WHICH IS NON-PERIODIC
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C
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IF (KSWX.EQ.1 .OR. (I.GT.1 .AND. I.LT.K)) GO TO 10
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TX = AI/3.0*(UXXXX/4.0+UXXX/DLX)
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10 IF (KSWY.EQ.1 .OR. (J.GT.1 .AND. J.LT.L)) GO TO 20
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TY = (UYYYY/4.0+UYYY/DLY)/3.0
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20 GRHS(I,J)=GRHS(I,J)+DLY**2*(DLX**2*TX+DLY**2*TY)
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30 CONTINUE
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C
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C RESET THE RIGHT HAND SIDE IN USOL
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C
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DO 60 I=IS,MS
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DO 50 J=JS,NS
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USOL(I,J) = GRHS(I,J)
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50 CONTINUE
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60 CONTINUE
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RETURN
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END
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