! D03PPF Example Program Text ! Mark 23 Release. NAG Copyright 2011. MODULE d03ppfe_mod ! D03PPF Example Program Module: ! Parameters and User-defined Routines ! .. Use Statements .. USE nag_library, ONLY : nag_wp ! .. Implicit None Statement .. IMPLICIT NONE ! .. Parameters .. REAL (KIND=nag_wp), PARAMETER :: four = 4.0_nag_wp REAL (KIND=nag_wp), PARAMETER :: half = 0.5_nag_wp REAL (KIND=nag_wp), PARAMETER :: one = 1.0_nag_wp REAL (KIND=nag_wp), PARAMETER :: ptone = 0.1_nag_wp REAL (KIND=nag_wp), PARAMETER :: two = 2.0_nag_wp REAL (KIND=nag_wp), PARAMETER :: zero = 0.0_nag_wp INTEGER, PARAMETER :: itrace = 0, m = 0, ncode = 0, & nin = 5, nout = 6, npde = 1, & nxfix = 0, nxi = 0 ! .. Local Scalars .. REAL (KIND=nag_wp) :: e CONTAINS SUBROUTINE uvinit(npde,npts,nxi,x,xi,u,ncode,v) ! .. Implicit None Statement .. IMPLICIT NONE ! .. Scalar Arguments .. INTEGER, INTENT (IN) :: ncode, npde, npts, nxi ! .. Array Arguments .. REAL (KIND=nag_wp), INTENT (OUT) :: u(npde,npts), v(ncode) REAL (KIND=nag_wp), INTENT (IN) :: x(npts), xi(nxi) ! .. Local Scalars .. REAL (KIND=nag_wp) :: a, b, c, t INTEGER :: i ! .. Intrinsic Functions .. INTRINSIC exp ! .. Executable Statements .. t = zero DO i = 1, npts a = (x(i)-0.25_nag_wp-0.75_nag_wp*t)/(four*e) b = (0.9_nag_wp*x(i)-0.325_nag_wp-0.495_nag_wp*t)/(two*e) IF (a>zero .AND. a>b) THEN a = exp(-a) c = (0.8_nag_wp*x(i)-0.4_nag_wp-0.24_nag_wp*t)/(four*e) c = exp(c) u(1,i) = (half+ptone*c+a)/(one+c+a) ELSE IF (b>zero .AND. b>=a) THEN b = exp(-b) c = (-0.8_nag_wp*x(i)+0.4_nag_wp+0.24_nag_wp*t)/(four*e) c = exp(c) u(1,i) = (ptone+half*c+b)/(one+c+b) ELSE a = exp(a) b = exp(b) u(1,i) = (one+half*a+ptone*b)/(one+a+b) END IF END DO RETURN END SUBROUTINE uvinit SUBROUTINE pdedef(npde,t,x,u,ux,ncode,v,vdot,p,q,r,ires) ! .. Implicit None Statement .. IMPLICIT NONE ! .. Scalar Arguments .. REAL (KIND=nag_wp), INTENT (IN) :: t, x INTEGER, INTENT (INOUT) :: ires INTEGER, INTENT (IN) :: ncode, npde ! .. Array Arguments .. REAL (KIND=nag_wp), INTENT (OUT) :: p(npde,npde), q(npde), r(npde) REAL (KIND=nag_wp), INTENT (IN) :: u(npde), ux(npde), v(ncode), & vdot(ncode) ! .. Executable Statements .. p(1,1) = one r(1) = e*ux(1) q(1) = u(1)*ux(1) RETURN END SUBROUTINE pdedef SUBROUTINE bndary(npde,t,u,ux,ncode,v,vdot,ibnd,beta,gamma,ires) ! .. Implicit None Statement .. IMPLICIT NONE ! .. Scalar Arguments .. REAL (KIND=nag_wp), INTENT (IN) :: t INTEGER, INTENT (IN) :: ibnd, ncode, npde INTEGER, INTENT (INOUT) :: ires ! .. Array Arguments .. REAL (KIND=nag_wp), INTENT (OUT) :: beta(npde), gamma(npde) REAL (KIND=nag_wp), INTENT (IN) :: u(npde), ux(npde), v(ncode), & vdot(ncode) ! .. Local Scalars .. REAL (KIND=nag_wp) :: a, b, c, ue, x ! .. Intrinsic Functions .. INTRINSIC exp ! .. Executable Statements .. beta(1) = zero IF (ibnd==0) THEN x = zero a = (x-0.25_nag_wp-0.75_nag_wp*t)/(four*e) b = (0.9_nag_wp*x-0.325_nag_wp-0.495_nag_wp*t)/(two*e) IF (a>zero .AND. a>b) THEN a = exp(-a) c = (0.8_nag_wp*x-0.4_nag_wp-0.24_nag_wp*t)/(four*e) c = exp(c) ue = (half+ptone*c+a)/(one+c+a) ELSE IF (b>zero .AND. b>=a) THEN b = exp(-b) c = (-0.8_nag_wp*x+0.4_nag_wp+0.24_nag_wp*t)/(four*e) c = exp(c) ue = (ptone+half*c+b)/(one+c+b) ELSE a = exp(a) b = exp(b) ue = (one+half*a+ptone*b)/(one+a+b) END IF ELSE x = one a = (x-0.25_nag_wp-0.75_nag_wp*t)/(four*e) b = (0.9_nag_wp*x-0.325_nag_wp-0.495_nag_wp*t)/(two*e) IF (a>zero .AND. a>b) THEN a = exp(-a) c = (0.8_nag_wp*x-0.4_nag_wp-0.24_nag_wp*t)/(four*e) c = exp(c) ue = (half+ptone*c+a)/(one+c+a) ELSE IF (b>zero .AND. b>=a) THEN b = exp(-b) c = (-0.8_nag_wp*x+0.4_nag_wp+0.24_nag_wp*t)/(four*e) c = exp(c) ue = (ptone+half*c+b)/(one+c+b) ELSE a = exp(a) b = exp(b) ue = (one+half*a+ptone*b)/(one+a+b) END IF END IF gamma(1) = u(1) - ue RETURN END SUBROUTINE bndary SUBROUTINE monitf(t,npts,npde,x,u,r,fmon) ! .. Implicit None Statement .. IMPLICIT NONE ! .. Scalar Arguments .. REAL (KIND=nag_wp), INTENT (IN) :: t INTEGER, INTENT (IN) :: npde, npts ! .. Array Arguments .. REAL (KIND=nag_wp), INTENT (OUT) :: fmon(npts) REAL (KIND=nag_wp), INTENT (IN) :: r(npde,npts), u(npde,npts), & x(npts) ! .. Local Scalars .. REAL (KIND=nag_wp) :: drdx, h INTEGER :: i ! .. Intrinsic Functions .. INTRINSIC abs ! .. Executable Statements .. fmon(1) = abs((r(1,2)-r(1,1))/((x(2)-x(1))*half)) DO i = 2, npts - 1 h = (x(i+1)-x(i-1))*half ! Second derivative .. drdx = (r(1,i+1)-r(1,i))/h fmon(i) = abs(drdx) END DO fmon(npts) = fmon(npts-1) RETURN END SUBROUTINE monitf SUBROUTINE exact(t,x,npts,u) ! Exact solution (for comparison purposes) ! .. Implicit None Statement .. IMPLICIT NONE ! .. Scalar Arguments .. REAL (KIND=nag_wp), INTENT (IN) :: t INTEGER, INTENT (IN) :: npts ! .. Array Arguments .. REAL (KIND=nag_wp), INTENT (OUT) :: u(npts) REAL (KIND=nag_wp), INTENT (IN) :: x(npts) ! .. Local Scalars .. REAL (KIND=nag_wp) :: a, b, c INTEGER :: i ! .. Intrinsic Functions .. INTRINSIC exp ! .. Executable Statements .. DO i = 1, npts a = (x(i)-0.25_nag_wp-0.75_nag_wp*t)/(four*e) b = (0.9_nag_wp*x(i)-0.325_nag_wp-0.495_nag_wp*t)/(two*e) IF (a>zero .AND. a>b) THEN a = exp(-a) c = (0.8_nag_wp*x(i)-0.4_nag_wp-0.24_nag_wp*t)/(four*e) c = exp(c) u(i) = (half+ptone*c+a)/(one+c+a) ELSE IF (b>zero .AND. b>=a) THEN b = exp(-b) c = (-0.8_nag_wp*x(i)+0.4_nag_wp+0.24_nag_wp*t)/(four*e) c = exp(c) u(i) = (ptone+half*c+b)/(one+c+b) ELSE a = exp(a) b = exp(b) u(i) = (one+half*a+ptone*b)/(one+a+b) END IF END DO RETURN END SUBROUTINE exact END MODULE d03ppfe_mod PROGRAM d03ppfe ! D03PPF Example Main Program ! .. Use Statements .. USE nag_library, ONLY : d03pck, d03ppf, d03pzf USE d03ppfe_mod, ONLY : bndary, e, exact, half, itrace, m, monitf, & nag_wp, ncode, nin, nout, npde, nxfix, nxi, & pdedef, two, uvinit, zero ! .. Implicit None Statement .. IMPLICIT NONE ! .. Local Scalars .. REAL (KIND=nag_wp) :: con, dx, dxmesh, tout, trmesh, & ts, x0, xmid, xratio INTEGER :: i, ifail, ind, intpts, ipminf, & it, itask, itol, itype, lenode, & lisave, lrsave, neqn, npts, & nrmesh, nwkres LOGICAL :: remesh, theta CHARACTER (1) :: laopt, norm ! .. Local Arrays .. REAL (KIND=nag_wp) :: algopt(30), atol(1), rtol(1), & xfix(1), xi(1) REAL (KIND=nag_wp), ALLOCATABLE :: rsave(:), u(:), ue(:), & uout(:,:,:), x(:), xout(:) INTEGER, ALLOCATABLE :: isave(:) ! .. Intrinsic Functions .. INTRINSIC min, real ! .. Executable Statements .. WRITE (nout,*) 'D03PPF Example Program Results' ! Skip heading in data file READ (nin,*) READ (nin,*) npts, intpts, itype lisave = 25 + nxfix neqn = npde*npts + ncode nwkres = npde*(npts+3*npde+21) + 7*npts + nxfix + 3 lenode = 11*neqn + 50 lrsave = neqn*neqn + neqn + nwkres + lenode ALLOCATE (u(neqn),ue(intpts),uout(npde,intpts,itype),rsave(lrsave), & x(npts),xout(intpts),isave(lisave)) READ (nin,*) itol READ (nin,*) atol(1), rtol(1) READ (nin,*) e ! Initialise mesh DO i = 1, npts x(i) = real(i-1,kind=nag_wp)/real(npts-1,kind=nag_wp) END DO ! Set remesh parameters remesh = .TRUE. nrmesh = 3 dxmesh = half con = two/real(npts-1,kind=nag_wp) xratio = 1.5_nag_wp ipminf = 0 xi(1) = zero norm = 'A' laopt = 'F' ind = 0 itask = 1 ! Set theta to .TRUE. if the Theta integrator is required theta = .FALSE. algopt(1:30) = zero IF (theta) THEN algopt(1) = two ELSE algopt(1) = zero END IF ! Loop over output value of t ts = zero tout = zero DO it = 1, 5 xmid = half + half*tout tout = 0.2_nag_wp*real(it,kind=nag_wp) ! ifail: behaviour on error exit ! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft ifail = 0 CALL d03ppf(npde,m,ts,tout,pdedef,bndary,uvinit,u,npts,x,ncode, & d03pck,nxi,xi,neqn,rtol,atol,itol,norm,laopt,algopt,remesh,nxfix, & xfix,nrmesh,dxmesh,trmesh,ipminf,xratio,con,monitf,rsave,lrsave, & isave,lisave,itask,itrace,ind,ifail) IF (it==1) THEN WRITE (nout,99998) atol, npts WRITE (nout,99993) nrmesh WRITE (nout,99992) e WRITE (nout,*) END IF ! Set output points .. dx = 0.1_nag_wp IF (tout>half) dx = 0.05_nag_wp x0 = xmid - half*real(intpts-1,kind=nag_wp)*dx DO i = 1, intpts xout(i) = x0 x0 = x0 + dx END DO xout(intpts) = min(xout(intpts),x(npts)) WRITE (nout,99999) ts WRITE (nout,99996) xout(1:intpts) ! Interpolate at output points .. ifail = 0 CALL d03pzf(npde,m,u,npts,x,xout,intpts,itype,uout,ifail) ! Check against exact solution .. CALL exact(ts,xout,intpts,ue) WRITE (nout,99995) uout(1,1:intpts,1) WRITE (nout,99994) ue(1:intpts) END DO WRITE (nout,99997) isave(1), isave(2), isave(3), isave(5) 99999 FORMAT (' T = ',F6.3) 99998 FORMAT (//' Accuracy requirement =',E10.3,' Number of points = ',I3/) 99997 FORMAT (' Number of integration steps in time = ',I6/' Number o', & 'f function evaluations = ',I6/' Number of Jacobian eval', & 'uations =',I6/' Number of iterations = ',I6) 99996 FORMAT (1X,'X ',5F9.4) 99995 FORMAT (1X,'Approx sol. ',5F9.4) 99994 FORMAT (1X,'Exact sol. ',5F9.4/) 99993 FORMAT (2X,'Remeshing every',I3,' time steps'/) 99992 FORMAT (2X,'E =',F8.3) END PROGRAM d03ppfe