C * * * * * * * * * * * * * * * * * * * * * * * * * C --- DRIVER FOR DOPRI5 ON VAN DER POL'S EQUATION C * * * * * * * * * * * * * * * * * * * * * * * * * cfeh dr_dop853 dop853 include 'dop853.f' IMPLICIT REAL*8 (A-H,O-Z) PARAMETER (NDGL=2,NRD=2) PARAMETER (LWORK=11*NDGL+8*NRD+21,LIWORK=NRD+21) DIMENSION Y(NDGL),WORK(LWORK),IWORK(LIWORK) EXTERNAL FVPOL,SOLOUT C --- DIMENSION OF THE SYSTEM N=2 RPAR=1.0D-3 C --- OUTPUT ROUTINE (AND DENSE OUTPUT) IS USED DURING INTEGRATION IOUT=3 C --- INITIAL VALUES X=0.0D0 Y(1)=2.0D0 Y(2)=0.0D0 C --- ENDPOINT OF INTEGRATION XEND=2.0D0 C --- REQUIRED (RELATIVE) TOLERANCE TOL=1.0D-9 ITOL=0 RTOL=TOL ATOL=TOL C --- DEFAULT VALUES FOR PARAMETERS DO 10 I=1,10 IWORK(I)=0 10 WORK(I)=0.D0 IWORK(5)=N IWORK(4)=1 C --- CALL OF THE SUBROUTINE DOPRI8 CALL DOP853(N,FVPOL,X,Y,XEND, & RTOL,ATOL,ITOL, & SOLOUT,IOUT, & WORK,LWORK,IWORK,LIWORK,RPAR,IPAR,IDID) C --- PRINT FINAL SOLUTION WRITE (6,99) X,Y(1),Y(2) 99 FORMAT(1X,'X =',F5.2,' Y =',2E18.10) C --- PRINT STATISTICS WRITE (6,90) TOL 90 FORMAT(' tol=',D8.2) WRITE (6,91) (IWORK(J),J=17,20) 91 FORMAT(' fcn=',I5,' step=',I4,' accpt=',I4,' rejct=',I3) STOP END C SUBROUTINE SOLOUT (NR,XOLD,X,Y,N,CON,ICOMP,ND, & RPAR,IPAR,IRTRN,XOUT) C --- PRINTS SOLUTION AT EQUIDISTANT OUTPUT-POINTS C --- BY USING "CONTD8", THE CONTINUOUS COLLOCATION SOLUTION IMPLICIT REAL*8 (A-H,O-Z) DIMENSION Y(N),CON(8*ND),ICOMP(ND) IF (NR.EQ.1) THEN WRITE (6,99) X,Y(1),Y(2),NR-1 XOUT=0.1D0 ELSE 10 CONTINUE IF (X.GE.XOUT) THEN WRITE (6,99) XOUT,CONTD8(1,XOUT,CON,ICOMP,ND), & CONTD8(2,XOUT,CON,ICOMP,ND),NR-1 XOUT=XOUT+0.1D0 GOTO 10 END IF END IF 99 FORMAT(1X,'X =',F5.2,' Y =',2E18.10,' NSTEP =',I4) RETURN END C SUBROUTINE FVPOL(N,X,Y,F,RPAR,IPAR) C --- RIGHT-HAND SIDE OF VAN DER POL'S EQUATION IMPLICIT REAL*8 (A-H,O-Z) DIMENSION Y(N),F(N) EPS=RPAR F(1)=Y(2) F(2)=((1-Y(1)**2)*Y(2)-Y(1))/EPS RETURN END