! D02NGF Example Program Text
! Mark 28.3 Release. NAG Copyright 2022.
Module d02ngfe_mod
! D02NGF 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, neq = 3, &
nin = 5, nout = 6
Integer, Parameter, Public :: nrw = 50 + 4*neq
Integer, Parameter, Public :: nwkjac = neq*(neq+1)
Integer, Parameter, Public :: print_stats = 0
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)
r(2) = -ydot(2)
r(3) = -ydot(3)
If (ires==1) Then
r(1) = -alpha*y(1) + beta*y(2)*y(3) + 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 d02ngfe_mod
Program d02ngfe
! D02NGF Example Main Program
! .. Use Statements ..
Use d02ngfe_mod, Only: iset, itrace, ldysav, neq, nin, nout, nrw, &
nwkjac, print_stats, resid
Use nag_library, Only: d02nby, d02ngf, d02ngz, d02nsf, d02nvf, d02nyf, &
d02xjf, nag_wp, x04abf
! .. Implicit None Statement ..
Implicit None
! .. Local Scalars ..
Real (Kind=nag_wp) :: h, h0, hmax, hmin, hu, t, tcrit, &
tcur, tolsf, tout, xout
Integer :: i, ifail, imxer, iout, 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(:), sol(:), &
wkjac(:), y(:), ydot(:), ysav(:,:)
Real (Kind=nag_wp) :: con(6)
Integer :: inform(23)
Logical, Allocatable :: algequ(:)
Logical :: lderiv(2)
! .. Intrinsic Procedures ..
Intrinsic :: real
! .. Executable Statements ..
Write (nout,*) 'D02NGF Example Program Results'
! Skip heading in data file
Read (nin,*)
Read (nin,*) maxord, maxstp, mxhnil
sdysav = maxord + 1
Allocate (atol(neq),rtol(neq),rwork(nrw),sol(neq),wkjac(nwkjac),y(neq), &
ydot(neq),ysav(ldysav,sdysav),algequ(neq))
outchn = nout
Call x04abf(iset,outchn)
! Integrate to tout by overshooting tout in one step mode (itask=2)
! using B.D.F formulae with a functional iteration method.
! Default values for the array con are used. Employ vector
! tolerances and the Jacobian is evaluated internally, if necessary.
! monitr subroutine replaced by NAG dummy routine D02NBY.
! Interpolation outside D02NGF using D02XJF.
itask = 2
Read (nin,*) petzld
Read (nin,*) hmin, hmax, h0, tcrit
Read (nin,*) t, tout
Read (nin,*) y(1:neq)
Read (nin,*) lderiv(1:2)
Read (nin,*) itol
Read (nin,*) rtol(1:neq)
Read (nin,*) atol(1:neq)
con(1:6) = 0.0_nag_wp
! ifail: behaviour on error exit
! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call d02nvf(neq,sdysav,maxord,'Functional-iteration',petzld,con,tcrit, &
hmin,hmax,h0,maxstp,mxhnil,'Average-L2',rwork,ifail)
! Linear algebra setup required (in case functional iteration
! encounters any difficulty).
ifail = 0
Call d02nsf(neq,neq,'Numerical',nwkjac,rwork,ifail)
xout = 0.02E0_nag_wp
iout = 1
Write (nout,99993)(i,i=1,neq)
Write (nout,99999) t, (y(i),i=1,neq)
! Soft fail and error messages only
loop1: Do
ifail = -1
Call d02ngf(neq,ldysav,t,tout,y,ydot,rwork,rtol,atol,itol,inform, &
resid,ysav,sdysav,d02ngz,wkjac,nwkjac,d02nby,lderiv,itask,itrace, &
ifail)
If (ifail==0) Then
ifail = 0
Call d02nyf(neq,neq,hu,h,tcur,tolsf,rwork,nst,nre,nje,nqu,nq,niter, &
imxer,algequ,inform,ifail)
loop2: Do
If (tcur-hu<xout .And. xout<=tcur) Then
! C0 interpolation
ifail = 0
Call d02xjf(xout,sol,neq,ysav,ldysav,sdysav,neq,tcur,nqu,hu,h, &
ifail)
Write (nout,99999) xout, (sol(i),i=1,neq)
iout = iout + 1
xout = real(iout,kind=nag_wp)*0.02E0_nag_wp
If (iout>=6) Then
If (print_stats>0) Then
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
End If
Exit loop1
End If
Else
Exit loop2
End If
End Do loop2
Else
Write (nout,*)
Write (nout,99998) 'Exit D02NGF with IFAIL = ', ifail, ' and T = ', &
t
End If
End Do loop1
99999 Format (1X,F8.3,3(F13.5,2X))
99998 Format (1X,A,I2,A,E12.5)
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 d02ngfe