! D02TYF Example Program Text ! Mark 24 Release. NAG Copyright 2012. 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) ! .. 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 Procedures .. 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) ! .. 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 Procedures .. 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) ! .. 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) ! .. 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) ! .. 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) ! .. 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) ! .. 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, nag_wp Use d02tyfe_mod, Only: a, ffun, fjac, gafun, gajac, gbfun, gbjac, guess, & m, mmax, 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 Procedures .. 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