! D02NHF Example Program Text
! Mark 30.0 Release. NAG Copyright 2024.
Module d02nhfe_mod
! D02NHF Example Program Module:
! Parameters and User-defined Routines
! .. Use Statements ..
Use nag_library, Only: nag_wp
! .. Implicit None Statement ..
Implicit None
! .. Accessibility Statements ..
Private
Public :: resid
! .. Parameters ..
Real (Kind=nag_wp), Parameter :: alpha = 0.04_nag_wp
Real (Kind=nag_wp), Parameter :: beta = 1.0E4_nag_wp
Real (Kind=nag_wp), Parameter :: gamma = 3.0E7_nag_wp
Integer, Parameter, Public :: iset = 1, itrace = 0, ml = 1, &
mu = 2, neq = 3, nin = 5
Integer, Parameter, Public :: njcpvt = neq
Integer, Parameter, Public :: nout = 6
Integer, Parameter, Public :: nrw = 50 + 4*neq
Integer, Parameter, Public :: nwkjac = neq*(2*ml+mu+1)
Integer, Parameter, Public :: ldysav = neq
Contains
Subroutine resid(neq,t,y,ydot,r,ires)
! .. Scalar Arguments ..
Real (Kind=nag_wp), Intent (In) :: t
Integer, Intent (Inout) :: ires
Integer, Intent (In) :: neq
! .. Array Arguments ..
Real (Kind=nag_wp), Intent (Out) :: r(neq)
Real (Kind=nag_wp), Intent (In) :: y(neq), ydot(neq)
! .. Executable Statements ..
r(1) = -ydot(1) - ydot(2) - ydot(3)
r(2) = -ydot(2)
r(3) = -ydot(3)
If (ires==1) Then
r(1) = r(1)
r(2) = alpha*y(1) - beta*y(2)*y(3) - gamma*y(2)*y(2) + r(2)
r(3) = gamma*y(2)*y(2) + r(3)
End If
Return
End Subroutine resid
End Module d02nhfe_mod
Program d02nhfe
! D02NHF Example Main Program
! .. Use Statements ..
Use d02nhfe_mod, Only: iset, itrace, ldysav, ml, mu, neq, nin, njcpvt, &
nout, nrw, nwkjac, resid
Use nag_library, Only: d02nby, d02nhf, d02nhz, d02ntf, d02nvf, d02nyf, &
nag_wp, x04abf
! .. Implicit None Statement ..
Implicit None
! .. Local Scalars ..
Real (Kind=nag_wp) :: h, h0, hmax, hmin, hu, t, tcrit, &
tcur, tolsf, tout, tout1
Integer :: i, ifail, imxer, itask, itol, &
maxord, maxstp, mxhnil, niter, nje, &
nq, nqu, nre, nst, outchn, sdysav
Logical :: petzld
! .. Local Arrays ..
Real (Kind=nag_wp), Allocatable :: atol(:), rtol(:), rwork(:), &
wkjac(:), y(:), ydot(:), ysav(:,:)
Real (Kind=nag_wp) :: con(6)
Integer :: inform(23)
Integer, Allocatable :: jacpvt(:)
Logical, Allocatable :: algequ(:)
Logical :: lderiv(2)
! .. Executable Statements ..
Write (nout,*) 'D02NHF Example Program Results'
Flush (nout)
! Skip heading in data file
Read (nin,*)
Read (nin,*) maxord, maxstp, mxhnil
sdysav = maxord + 1
Allocate (atol(neq),rtol(neq),rwork(nrw),wkjac(nwkjac),y(neq),ydot(neq), &
ysav(ldysav,sdysav),jacpvt(njcpvt),algequ(neq))
outchn = nout
Call x04abf(iset,outchn)
! Set itask=6 to provide initial estimates of solution and its
! time derivative. Default values for the array con are used.
! Use the B.D.F. formulae with a Newton method.
! Employ scalar relative tolerance and vector absolute tolerance.
! The Jacobian is evaluated internally.
! monitr subroutine replaced by NAG dummy routine D02NBY.
Read (nin,*) hmin, hmax, h0, tcrit
Read (nin,*) petzld
Read (nin,*) t, tout1
Read (nin,*) y(1:neq)
Read (nin,*) lderiv(1:2)
Read (nin,*) itol
Read (nin,*) rtol(1)
Read (nin,*) atol(1:neq)
itask = 6
tout = tout1
con(1:6) = 0.0_nag_wp
ifail = 0
Call d02nvf(neq,sdysav,maxord,'Newton',petzld,con,tcrit,hmin,hmax,h0, &
maxstp,mxhnil,'Average-L2',rwork,ifail)
ifail = 0
Call d02ntf(neq,neq,'Numerical',ml,mu,nwkjac,njcpvt,rwork,ifail)
! Hard fail on initial and subsequent tasks.
ifail = 0
Call d02nhf(neq,ldysav,t,tout,y,ydot,rwork,rtol,atol,itol,inform,resid, &
ysav,sdysav,d02nhz,wkjac,nwkjac,jacpvt,njcpvt,d02nby,lderiv,itask, &
itrace,ifail)
Write (nout,*)
Write (nout,99999) ' Initial Y : ', y(1:neq)
Write (nout,99999) ' Initial YDOT : ', ydot(1:neq)
Flush (nout)
! Use these initial estimates and integrate to tout (overshoot and
! interpolate)
itask = 1
tout = tout1
ifail = 0
Call d02nhf(neq,ldysav,t,tout,y,ydot,rwork,rtol,atol,itol,inform,resid, &
ysav,sdysav,d02nhz,wkjac,nwkjac,jacpvt,njcpvt,d02nby,lderiv,itask, &
itrace,ifail)
Write (nout,99993)(i,i=1,neq)
Write (nout,99998) tout, y(1:neq)
ifail = 0
Call d02nyf(neq,neq,hu,h,tcur,tolsf,rwork,nst,nre,nje,nqu,nq,niter, &
imxer,algequ,inform,ifail)
Write (nout,*)
Write (nout,99997) hu, h, tcur
Write (nout,99996) nst, nre, nje
Write (nout,99995) nqu, nq, niter
Write (nout,99994) ' Max err comp = ', imxer
99999 Format (1X,A,3(F11.4,2X))
99998 Format (1X,F8.3,3(F13.5,2X))
99997 Format (1X,' HUSED = ',E12.5,' HNEXT = ',E12.5,' TCUR = ',E12.5)
99996 Format (1X,' NST = ',I6,' NRE = ',I6,' NJE = ',I6)
99995 Format (1X,' NQU = ',I6,' NQ = ',I6,' NITER = ',I6)
99994 Format (1X,A,I4)
99993 Format (/,1X,' X ',3(' Y(',I1,') '))
End Program d02nhfe