! D03PDA Example Program Text
! Mark 30.3 Release. nAG Copyright 2024.
Module d03pdae_mod
! D03PDA 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 :: bndary, pdedef, uinit
! .. Parameters ..
Integer, Parameter, Public :: nin = 5, nout = 6, npde = 2
Contains
Subroutine pdedef(npde,t,x,nptl,u,ux,p,q,r,ires,iuser,ruser)
! .. Scalar Arguments ..
Real (Kind=nag_wp), Intent (In) :: t
Integer, Intent (Inout) :: ires
Integer, Intent (In) :: npde, nptl
! .. Array Arguments ..
Real (Kind=nag_wp), Intent (Out) :: p(npde,npde,nptl), q(npde,nptl), &
r(npde,nptl)
Real (Kind=nag_wp), Intent (Inout) :: ruser(*)
Real (Kind=nag_wp), Intent (In) :: u(npde,nptl), ux(npde,nptl), &
x(nptl)
Integer, Intent (Inout) :: iuser(*)
! .. Local Scalars ..
Integer :: i
! .. Executable Statements ..
Do i = 1, nptl
q(1,i) = u(2,i)
q(2,i) = u(1,i)*ux(2,i) - ux(1,i)*u(2,i)
r(1,i) = ux(1,i)
r(2,i) = ux(2,i)
p(1,1:2,i) = 0.0_nag_wp
p(2,1,i) = 0.0_nag_wp
p(2,2,i) = 1.0_nag_wp
End Do
Return
End Subroutine pdedef
Subroutine bndary(npde,t,u,ux,ibnd,beta,gamma,ires,iuser,ruser)
! .. Scalar Arguments ..
Real (Kind=nag_wp), Intent (In) :: t
Integer, Intent (In) :: ibnd, npde
Integer, Intent (Inout) :: ires
! .. Array Arguments ..
Real (Kind=nag_wp), Intent (Out) :: beta(npde), gamma(npde)
Real (Kind=nag_wp), Intent (Inout) :: ruser(*)
Real (Kind=nag_wp), Intent (In) :: u(npde), ux(npde)
Integer, Intent (Inout) :: iuser(*)
! .. Executable Statements ..
If (ibnd==0) Then
beta(1) = 1.0_nag_wp
gamma(1) = 0.0_nag_wp
beta(2) = 0.0_nag_wp
gamma(2) = u(1) - 1.0_nag_wp
Else
beta(1) = 1.0_nag_wp
gamma(1) = 0.0_nag_wp
beta(2) = 0.0_nag_wp
gamma(2) = u(1) + 1.0_nag_wp
End If
Return
End Subroutine bndary
Subroutine uinit(npde,npts,x,u,iuser,ruser)
! .. Scalar Arguments ..
Integer, Intent (In) :: npde, npts
! .. Array Arguments ..
Real (Kind=nag_wp), Intent (Inout) :: ruser(*)
Real (Kind=nag_wp), Intent (Out) :: u(npde,npts)
Real (Kind=nag_wp), Intent (In) :: x(npts)
Integer, Intent (Inout) :: iuser(*)
! .. Local Scalars ..
Real (Kind=nag_wp) :: piby2
Integer :: i
! .. Intrinsic Procedures ..
Intrinsic :: sin
! .. Executable Statements ..
piby2 = ruser(1)
Do i = 1, npts
u(1,i) = -sin(piby2*x(i))
u(2,i) = -piby2*piby2*u(1,i)
End Do
Return
End Subroutine uinit
End Module d03pdae_mod
Program d03pdae
! D03PDA Example Main Program
! .. Use Statements ..
Use d03pdae_mod, Only: bndary, nin, nout, npde, pdedef, uinit
Use nag_library, Only: d03pda, d03pyf, nag_wp, x01aaf
! .. Implicit None Statement ..
Implicit None
! .. Local Scalars ..
Real (Kind=nag_wp) :: acc, dx, pi, piby2, tout, ts
Integer :: i, ifail, ind, intpts, it, itask, &
itrace, itype, lenode, m, mu, &
nbkpts, nel, neqn, niw, npl1, npoly, &
npts, nw, nwkres
! .. Local Arrays ..
Real (Kind=nag_wp) :: ruser(1), rwsav(1100)
Real (Kind=nag_wp), Allocatable :: u(:,:), uout(:,:,:), w(:), x(:), &
xbkpts(:), xout(:)
Integer :: iuser(1), iwsav(505)
Integer, Allocatable :: iw(:)
Logical :: lwsav(100)
Character (80) :: cwsav(10)
! .. Intrinsic Procedures ..
Intrinsic :: real
! .. Executable Statements ..
Write (nout,*) 'D03PDA Example Program Results'
! Skip heading in data file
Read (nin,*)
Read (nin,*) intpts, nbkpts, npoly, itype
nel = nbkpts - 1
npts = nel*npoly + 1
mu = npde*(npoly+1) - 1
neqn = npde*npts
niw = neqn + 24
npl1 = npoly + 1
nwkres = 3*npl1*npl1 + npl1*(npde*npde+6*npde+nbkpts+1) + 13*npde + 5
lenode = (3*mu+1)*neqn
nw = 11*neqn + 50 + nwkres + lenode
Allocate (u(npde,npts),uout(npde,intpts,itype),w(nw),x(npts), &
xbkpts(nbkpts),xout(intpts),iw(niw))
Read (nin,*) xout(1:intpts)
Read (nin,*) acc
Read (nin,*) m, itrace
piby2 = 0.5_nag_wp*x01aaf(pi)
ruser(1) = piby2
! Set the break-points
dx = 2.0_nag_wp/real(nbkpts-1,kind=nag_wp)
xbkpts(1) = -1.0_nag_wp
Do i = 2, nbkpts - 1
xbkpts(i) = xbkpts(i-1) + dx
End Do
xbkpts(nbkpts) = 1.0_nag_wp
ind = 0
itask = 1
Read (nin,*) ts, tout
! Loop over output values of t
Do it = 1, 5
tout = 10.0_nag_wp*tout
! ifail: behaviour on error exit
! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call d03pda(npde,m,ts,tout,pdedef,bndary,u,nbkpts,xbkpts,npoly,npts,x, &
uinit,acc,w,nw,iw,niw,itask,itrace,ind,iuser,ruser,cwsav,lwsav, &
iwsav,rwsav,ifail)
If (it==1) Then
Write (nout,99999) npoly, nel
Write (nout,99998) acc, npts
Write (nout,99997) xout(1:6)
End If
! Interpolate at required spatial points
ifail = 0
Call d03pyf(npde,u,nbkpts,xbkpts,npoly,npts,xout,intpts,itype,uout,w, &
nw,ifail)
Write (nout,99996) ts, uout(1,1:intpts,1)
Write (nout,99995) uout(2,1:intpts,1)
End Do
! Print integration statistics
Write (nout,99994) iw(1), iw(2), iw(3), iw(5)
99999 Format (' Polynomial degree =',I4,' No. of elements = ',I4)
99998 Format (' Accuracy requirement =',E10.3,' Number of points = ',I5,/)
99997 Format (' T / X ',6F8.4,/)
99996 Format (1X,F7.4,' U(1)',6F8.4)
99995 Format (9X,'U(2)',6F8.4,/)
99994 Format (' Number of integration steps in time ',I4,/, &
' Number of residual evaluations of resulting ODE system',I4,/, &
' Number of Jacobian evaluations ',I4,/, &
' Number of iterations of nonlinear solver ',I4)
End Program d03pdae