! D02NCF Example Program Text
! Mark 26.2 Release. NAG Copyright 2017.
Module d02ncfe_mod
! D02NCF 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 :: fcn, jac
! .. 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
Real (Kind=nag_wp), Parameter :: one = 1.0_nag_wp
Real (Kind=nag_wp), Parameter :: two = 2.0_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 fcn(neq,t,y,f,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) :: f(neq)
Real (Kind=nag_wp), Intent (In) :: y(neq)
! .. Executable Statements ..
f(1) = -alpha*y(1) + beta*y(2)*y(3)
f(2) = alpha*y(1) - beta*y(2)*y(3) - gamma*y(2)*y(2)
f(3) = gamma*y(2)*y(2)
Return
End Subroutine fcn
Subroutine jac(neq,t,y,h,d,ml,mu,p)
! .. Scalar Arguments ..
Real (Kind=nag_wp), Intent (In) :: d, h, t
Integer, Intent (In) :: ml, mu, neq
! .. Array Arguments ..
Real (Kind=nag_wp), Intent (Inout) :: p(ml+mu+1,neq)
Real (Kind=nag_wp), Intent (In) :: y(neq)
! .. Local Scalars ..
Real (Kind=nag_wp) :: hxd
! .. Executable Statements ..
hxd = h*d
p(1,1) = one - hxd*(-alpha)
p(2,1) = -hxd*(beta*y(3))
p(3,1) = -hxd*(beta*y(2))
p(1,2) = -hxd*(alpha)
p(2,2) = one - hxd*(-beta*y(3)-two*gamma*y(2))
p(3,2) = -hxd*(-beta*y(2))
p(1,3) = -hxd*(two*gamma*y(2))
p(2,3) = one - hxd*(0.0_nag_wp)
Return
End Subroutine jac
End Module d02ncfe_mod
Program d02ncfe
! D02NCF Example Main Program
! .. Use Statements ..
Use d02ncfe_mod, Only: fcn, iset, itrace, jac, ldysav, ml, mu, neq, nin, &
njcpvt, nout, nrw, nwkjac
Use nag_library, Only: d02nby, d02ncf, d02ntf, d02nwf, d02nyf, d02nzf, &
nag_wp, x04abf
! .. Implicit None Statement ..
Implicit None
! .. Local Scalars ..
Real (Kind=nag_wp) :: h, h0, hmax, hmin, hu, t, tcrit, &
tcur, tolsf, tout
Integer :: i, ifail, imxer, itask, itol, &
maxord, maxstp, mxhnil, niter, nje, &
nq, nqu, nre, nst, outchn, sdysav
! .. 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(:)
! .. Executable Statements ..
Write (nout,*) 'D02NCF Example Program Results'
! Skip heading in data file
Read (nin,*)
Read (nin,*) maxord, maxstp, mxhnil
sdysav = maxord + 3
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)
! Integrate to tout (itask=1 i.e. overshooting and internal interpolation)
! using the blend method. Default values for the array con are used.
! Employ scalar relative tolerance and vector absolute tolerance.
! The Jacobian is evaluated by jac.
! monitr subroutine replaced by NAG dummy routine D02NBY.
Read (nin,*) hmin, hmax, h0, tcrit
Read (nin,*) t, tout
Read (nin,*) itol
Read (nin,*) y(1:neq)
Read (nin,*) rtol(1)
Read (nin,*) atol(1:neq)
con(1:6) = 0.0_nag_wp
itask = 1
! ifail: behaviour on error exit
! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call d02nwf(neq,sdysav,maxord,con,tcrit,hmin,hmax,h0,maxstp,mxhnil, &
'Average-L2',rwork,ifail)
ifail = 0
Call d02ntf(neq,neq,'Analytical',ml,mu,nwkjac,njcpvt,rwork,ifail)
Write (nout,99993)(i,i=1,neq)
Write (nout,99999) t, (y(i),i=1,neq)
! Soft fail and error messages only
ifail = -1
Call d02ncf(neq,ldysav,t,tout,y,ydot,rwork,rtol,atol,itol,inform,fcn, &
ysav,sdysav,jac,wkjac,nwkjac,jacpvt,njcpvt,d02nby,itask,itrace,ifail)
If (ifail==0) Then
Write (nout,99999) t, (y(i),i=1,neq)
Else
Write (nout,*)
Write (nout,99998) 'Exit D02NCF with IFAIL = ', ifail, ' and T = ', t
End If
! Reset tout and call D02NZF to override internal choice for step size.
! No changes to other parameters.
h = 0.7_nag_wp
ifail = 0
Call d02nzf(neq,tcrit,h,hmin,hmax,maxstp,mxhnil,rwork,ifail)
tout = 10.0_nag_wp
ifail = -1
Call d02ncf(neq,ldysav,t,tout,y,ydot,rwork,rtol,atol,itol,inform,fcn, &
ysav,sdysav,jac,wkjac,nwkjac,jacpvt,njcpvt,d02nby,itask,itrace,ifail)
If (ifail==0) Then
Write (nout,99999) t, (y(i),i=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
Write (nout,*)
Else
Write (nout,*)
Write (nout,99998) 'Exit D02NCF with IFAIL = ', ifail, ' and T = ', t
End If
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 d02ncfe