! D02NBF Example Program Text
! Mark 28.3 Release. NAG Copyright 2022.
Module d02nbfe_mod
! D02NBF 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, neq = 3, &
nin = 5, nout = 6
Integer, Parameter, Public :: nrw = 50 + 4*neq
Integer, Parameter, Public :: nwkjac = neq*(neq+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,p)
! .. Scalar Arguments ..
Real (Kind=nag_wp), Intent (In) :: d, h, t
Integer, Intent (In) :: neq
! .. Array Arguments ..
Real (Kind=nag_wp), Intent (Inout) :: p(neq,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(1,2) = -hxd*(beta*y(3))
p(1,3) = -hxd*(beta*y(2))
p(2,1) = -hxd*(alpha)
p(2,2) = one - hxd*(-beta*y(3)-two*gamma*y(2))
p(2,3) = -hxd*(-beta*y(2))
! Do not need to set P(3,1) since Jacobian preset to zero
! P(3,1) = - HXD*(0.0E0)
p(3,2) = -hxd*(two*gamma*y(2))
p(3,3) = one - hxd*(0.0_nag_wp)
Return
End Subroutine jac
End Module d02nbfe_mod
Program d02nbfe
! D02NBF Example Main Program
! .. Use Statements ..
Use d02nbfe_mod, Only: fcn, iset, itrace, jac, ldysav, neq, nin, nout, &
nrw, nwkjac
Use nag_library, Only: d02nbf, d02nby, d02nbz, d02nsf, d02nvf, d02nyf, &
nag_wp, x04abf
! .. Implicit None Statement ..
Implicit None
! .. Local Scalars ..
Real (Kind=nag_wp) :: h, h0, hmax, hmin, hu, t, tcrit, &
tcur, tinit, tolsf, tout
Integer :: i, icase, 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(:), yinit(:), &
ysav(:,:)
Real (Kind=nag_wp) :: con(6)
Integer :: inform(23)
Logical, Allocatable :: algequ(:)
! .. Executable Statements ..
Write (nout,*) 'D02NBF 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),wkjac(nwkjac),y(neq), &
yinit(neq),ydot(neq),ysav(ldysav,sdysav),algequ(neq))
outchn = nout
Call x04abf(iset,outchn)
Read (nin,*) petzld
Read (nin,*) hmin, hmax, h0
Read (nin,*) tinit, tout
Read (nin,*) itol
Read (nin,*) yinit(1:neq)
Read (nin,*) rtol(1), atol(1)
! Two cases. In both cases:
! integrate to tout without passing tout;
! use B.D.F formulae with a Newton method;
! use default values for the array con;
! use scalar tolerances;
! use NAG dummy routine D02NBY in place of MONITR subroutine.
con(1:6) = 0.0_nag_wp
tcrit = tout
itask = 4
cases: Do icase = 1, 2
t = tinit
y(1:neq) = yinit(1:neq)
! ifail: behaviour on error exit
! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call d02nvf(neq,sdysav,maxord,'Newton',petzld,con,tcrit,hmin,hmax,h0, &
maxstp,mxhnil,'Average-L2',rwork,ifail)
Write (nout,*)
ifail = 0
Select Case (icase)
Case (1)
! First case. The Jacobian is evaluated internally.
Call d02nsf(neq,neq,'Numerical',nwkjac,rwork,ifail)
Write (nout,*) ' Numerical Jacobian'
Case (2)
! Second case. The Jacobian is evaluated by jac.
Call d02nsf(neq,neq,'Analytical',nwkjac,rwork,ifail)
Write (nout,*) ' Analytic Jacobian'
End Select
Write (nout,99993)(i,i=1,neq)
Write (nout,99999) t, y(1:neq)
! Soft fail and error messages only
ifail = -1
Select Case (icase)
Case (1)
Call d02nbf(neq,ldysav,t,tout,y,ydot,rwork,rtol,atol,itol,inform, &
fcn,ysav,sdysav,d02nbz,wkjac,nwkjac,d02nby,itask,itrace,ifail)
Case (2)
Call d02nbf(neq,ldysav,t,tout,y,ydot,rwork,rtol,atol,itol,inform, &
fcn,ysav,sdysav,jac,wkjac,nwkjac,d02nby,itask,itrace,ifail)
End Select
If (ifail==0) Then
Write (nout,99999) t, 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
Write (nout,*)
Else
Write (nout,*)
Write (nout,99998) 'Exit D02NBF with IFAIL = ', ifail, ' and T = ', &
t
End If
End Do cases
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 d02nbfe