! D02TYF Example Program Text ! Mark 23 Release. NAG Copyright 2011. MODULE d02tyfe_mod ! D02TYF Example Program Module: ! Parameters and User-defined Routines ! .. Use Statements .. USE nag_library, ONLY : nag_wp ! .. Implicit None Statement .. IMPLICIT NONE ! .. Parameters .. INTEGER, PARAMETER :: mmax = 2, neq = 1, nin = 5, & nlbc = 1, nmesh_out = 11, & nout = 6, nrbc = 1 ! .. Local Scalars .. REAL (KIND=nag_wp) :: a ! .. Local Arrays .. INTEGER :: m(1) = (/ 2/) CONTAINS SUBROUTINE ffun(x,y,neq,m,f) ! .. Implicit None Statement .. IMPLICIT NONE ! .. Scalar Arguments .. REAL (KIND=nag_wp), INTENT (IN) :: x INTEGER, INTENT (IN) :: neq ! .. Array Arguments .. REAL (KIND=nag_wp), INTENT (OUT) :: f(neq) REAL (KIND=nag_wp), INTENT (IN) :: y(neq,0:*) INTEGER, INTENT (IN) :: m(neq) ! .. Intrinsic Functions .. INTRINSIC sqrt ! .. Executable Statements .. IF (y(1,0)<=0.0E0_nag_wp) THEN f(1) = 0.0_nag_wp ELSE f(1) = (y(1,0))**1.5_nag_wp/sqrt(x) END IF RETURN END SUBROUTINE ffun SUBROUTINE fjac(x,y,neq,m,dfdy) ! .. Implicit None Statement .. IMPLICIT NONE ! .. Scalar Arguments .. REAL (KIND=nag_wp), INTENT (IN) :: x INTEGER, INTENT (IN) :: neq ! .. Array Arguments .. REAL (KIND=nag_wp), INTENT (INOUT) :: dfdy(neq,neq,0:*) REAL (KIND=nag_wp), INTENT (IN) :: y(neq,0:*) INTEGER, INTENT (IN) :: m(neq) ! .. Intrinsic Functions .. INTRINSIC sqrt ! .. Executable Statements .. IF (y(1,0)<=0.0E0_nag_wp) THEN dfdy(1,1,0) = 0.0_nag_wp ELSE dfdy(1,1,0) = 1.5_nag_wp*sqrt(y(1,0))/sqrt(x) END IF RETURN END SUBROUTINE fjac SUBROUTINE gafun(ya,neq,m,nlbc,ga) ! .. Implicit None Statement .. IMPLICIT NONE ! .. Scalar Arguments .. INTEGER, INTENT (IN) :: neq, nlbc ! .. Array Arguments .. REAL (KIND=nag_wp), INTENT (OUT) :: ga(nlbc) REAL (KIND=nag_wp), INTENT (IN) :: ya(neq,0:*) INTEGER, INTENT (IN) :: m(neq) ! .. Executable Statements .. ga(1) = ya(1,0) - 1.0_nag_wp RETURN END SUBROUTINE gafun SUBROUTINE gbfun(yb,neq,m,nrbc,gb) ! .. Implicit None Statement .. IMPLICIT NONE ! .. Scalar Arguments .. INTEGER, INTENT (IN) :: neq, nrbc ! .. Array Arguments .. REAL (KIND=nag_wp), INTENT (OUT) :: gb(nrbc) REAL (KIND=nag_wp), INTENT (IN) :: yb(neq,0:*) INTEGER, INTENT (IN) :: m(neq) ! .. Executable Statements .. gb(1) = yb(1,0) RETURN END SUBROUTINE gbfun SUBROUTINE gajac(ya,neq,m,nlbc,dgady) ! .. Implicit None Statement .. IMPLICIT NONE ! .. Scalar Arguments .. INTEGER, INTENT (IN) :: neq, nlbc ! .. Array Arguments .. REAL (KIND=nag_wp), INTENT (INOUT) :: dgady(nlbc,neq,0:*) REAL (KIND=nag_wp), INTENT (IN) :: ya(neq,0:*) INTEGER, INTENT (IN) :: m(neq) ! .. Executable Statements .. dgady(1,1,0) = 1.0_nag_wp RETURN END SUBROUTINE gajac SUBROUTINE gbjac(yb,neq,m,nrbc,dgbdy) ! .. Implicit None Statement .. IMPLICIT NONE ! .. Scalar Arguments .. INTEGER, INTENT (IN) :: neq, nrbc ! .. Array Arguments .. REAL (KIND=nag_wp), INTENT (INOUT) :: dgbdy(nrbc,neq,0:*) REAL (KIND=nag_wp), INTENT (IN) :: yb(neq,0:*) INTEGER, INTENT (IN) :: m(neq) ! .. Executable Statements .. dgbdy(1,1,0) = 1.0_nag_wp RETURN END SUBROUTINE gbjac SUBROUTINE guess(x,neq,m,y,dym) ! .. Implicit None Statement .. IMPLICIT NONE ! .. Scalar Arguments .. REAL (KIND=nag_wp), INTENT (IN) :: x INTEGER, INTENT (IN) :: neq ! .. Array Arguments .. REAL (KIND=nag_wp), INTENT (OUT) :: dym(neq) REAL (KIND=nag_wp), INTENT (INOUT) :: y(neq,0:*) INTEGER, INTENT (IN) :: m(neq) ! .. Executable Statements .. y(1,0) = 1.0_nag_wp - x/a y(1,1) = -1.0_nag_wp/a dym(1) = 0.0_nag_wp RETURN END SUBROUTINE guess END MODULE d02tyfe_mod PROGRAM d02tyfe ! D02TYF Example Main Program ! .. Use Statements .. USE nag_library, ONLY : d02tkf, d02tvf, d02tyf, d02tzf USE d02tyfe_mod, ONLY : a, ffun, fjac, gafun, gajac, gbfun, gbjac, & guess, m, mmax, nag_wp, neq, nin, nlbc, & nmesh_out, nout, nrbc ! .. Implicit None Statement .. IMPLICIT NONE ! .. Local Scalars .. REAL (KIND=nag_wp) :: ainc, ermx, x INTEGER :: i, iermx, ifail, ijermx, liwork, & lrwork, mxmesh, ncol, nmesh LOGICAL :: failed ! .. Local Arrays .. REAL (KIND=nag_wp), ALLOCATABLE :: mesh(:), rwork(:), tol(:), y(:,:) INTEGER, ALLOCATABLE :: ipmesh(:), iwork(:) ! .. Intrinsic Functions .. INTRINSIC real ! .. Executable Statements .. WRITE (nout,*) 'D02TYF Example Program Results' WRITE (nout,*) ! Skip heading in data file READ (nin,*) READ (nin,*) ncol, nmesh, mxmesh liwork = mxmesh*(11*neq+6) lrwork = mxmesh*(109*neq**2+78*neq+7) ALLOCATE (mesh(mxmesh),tol(neq),rwork(lrwork),y(neq,0:mmax-1), & ipmesh(mxmesh),iwork(liwork)) READ (nin,*) a READ (nin,*) tol(1:neq) ainc = a/real(nmesh-1,kind=nag_wp) mesh(1) = 0.0E0_nag_wp DO i = 2, nmesh - 1 mesh(i) = mesh(i-1) + ainc END DO mesh(nmesh) = a ipmesh(1) = 1 ipmesh(2:nmesh-1) = 2 ipmesh(nmesh) = 1 ! Initialize ifail = 0 CALL d02tvf(neq,m,nlbc,nrbc,ncol,tol,mxmesh,nmesh,mesh,ipmesh,rwork, & lrwork,iwork,liwork,ifail) WRITE (nout,99999) tol(1), a ! Solve ifail = -1 CALL d02tkf(ffun,fjac,gafun,gbfun,gajac,gbjac,guess,rwork,iwork,ifail) failed = ifail /= 0 ! Extract mesh. ifail = -1 CALL d02tzf(mxmesh,nmesh,mesh,ipmesh,ermx,iermx,ijermx,rwork,iwork, & ifail) IF (ifail/=1) THEN ! Print mesh statistics WRITE (nout,99998) nmesh, ermx, iermx, ijermx WRITE (nout,99997) (i,ipmesh(i),mesh(i),i=1,nmesh) END IF IF ( .NOT. failed) THEN ! Print solution on output mesh. WRITE (nout,99996) x = 0.0_nag_wp ainc = a/real(nmesh_out-1,kind=nag_wp) DO i = 1, nmesh_out ifail = 0 CALL d02tyf(x,y,neq,mmax,rwork,iwork,ifail) WRITE (nout,99995) x, y(1,0:1) x = x + ainc END DO END IF 99999 FORMAT (//' Tolerance = ',E8.1,' A = ',F8.2) 99998 FORMAT (/' Used a mesh of ',I4,' points'/' Maximum error = ',E10.2, & ' in interval ',I4,' for component ',I4/) 99997 FORMAT (/' Mesh points:'/4(I4,'(',I1,')',E11.4)) 99996 FORMAT (/' Computed solution'/' x solution derivative') 99995 FORMAT (' ',F8.2,2F11.5) END PROGRAM d02tyfe