! D02MVF Example Program Text ! Mark 24 Release. NAG Copyright 2012. Module d02mvfe_mod ! D02MVF 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 :: one = 1.0_nag_wp Real (Kind=nag_wp), Parameter :: two = 2.0_nag_wp Integer, Parameter :: iset = 1, neq = 6, nin = 5, & nout = 6 Integer, Parameter :: nrw = 50 + 4*neq Integer, Parameter :: nwkjac = neq*(neq+1) Integer, Parameter :: sdysav = 8 Integer, Parameter :: 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 .. If (ires==-1) Then r(1) = -ydot(1) r(2) = -ydot(2) r(3) = -ydot(3) r(4) = -ydot(4) r(5:6) = 0.0E0_nag_wp Else r(1) = y(3) - y(6)*y(1) - ydot(1) r(2) = y(4) - y(6)*y(2) - ydot(2) r(3) = -y(5)*y(1) - ydot(3) r(4) = -y(5)*y(2) - one - ydot(4) r(5) = y(1)*y(3) + y(2)*y(4) r(6) = y(1)**2 + y(2)**2 - one End If Return End Subroutine resid Subroutine jac(neq,t,y,ydot,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), ydot(neq) ! .. Local Scalars .. Real (Kind=nag_wp) :: hxd ! .. Executable Statements .. hxd = h*d p(1,1) = (one+hxd*y(6)) p(1,3) = -hxd p(1,6) = hxd*y(1) p(2,2) = (one+hxd*y(6)) p(2,4) = -hxd p(2,6) = hxd*y(2) p(3,1) = hxd*y(5) p(3,3) = one p(3,5) = hxd*y(1) p(4,2) = hxd*y(5) p(4,4) = one p(4,5) = hxd*y(2) p(5,1) = -hxd*y(3) p(5,2) = -hxd*y(4) p(5,3) = -hxd*y(1) p(5,4) = -hxd*y(2) p(6,1) = -two*hxd*y(1) p(6,2) = -two*hxd*y(2) Return End Subroutine jac End Module d02mvfe_mod Program d02mvfe ! D02MVF Example Main Program ! .. Use Statements .. Use nag_library, Only: d02mvf, d02nby, d02ngf, d02nsf, nag_wp, x04abf Use d02mvfe_mod, Only: iset, jac, ldysav, neq, nin, nout, nrw, nwkjac, & one, resid, sdysav ! .. Implicit None Statement .. Implicit None ! .. Local Scalars .. Real (Kind=nag_wp) :: h0, hmax, hmin, t, tcrit, tout Integer :: i, ifail, itask, itol, itrace, & maxord, maxstp, mxhnil, outchn ! .. Local Arrays .. Real (Kind=nag_wp), Allocatable :: atol(:), rtol(:), rwork(:), & wkjac(:), y(:), ydot(:), ysav(:,:) Real (Kind=nag_wp) :: con(3) Integer :: inform(23) Logical :: lderiv(2) ! .. Executable Statements .. Write (nout,*) 'D02MVF Example Program Results' ! Skip heading in data file Read (nin,*) ! Allocations based on number of differential equations (neq) Allocate (atol(neq),rtol(neq),rwork(nrw),wkjac(nwkjac),y(neq),ydot(neq), & ysav(ldysav,sdysav)) ! Read algorithmic parameters Read (nin,*) maxord, maxstp, mxhnil Read (nin,*) hmin, hmax, h0 Read (nin,*) rtol(1), atol(1) Read (nin,*) itrace, itol Read (nin,*) t, tout Read (nin,*) y(1:neq) Read (nin,*) itask ! Set initial derivatives and other values outchn = nout Call x04abf(iset,outchn) con(1:3) = 0.0_nag_wp ydot(1) = y(3) - y(6)*y(1) ydot(2) = y(4) - y(6)*y(2) ydot(3) = -y(5)*y(1) ydot(4) = -y(5)*y(2) - one ydot(5) = -3.0_nag_wp*y(4) ydot(6) = 0.0_nag_wp tcrit = tout ! ifail: behaviour on error exit ! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft ifail = 0 Call d02mvf(neq,sdysav,maxord,con,tcrit,hmin,hmax,h0,maxstp,mxhnil, & 'AVERAGE-L2',rwork,ifail) Write (nout,*) Write (nout,99999) 'Pendulum problem with relative tolerance', rtol(1) Write (nout,99999) ' and absolute tolerance', atol(1) Write (nout,99998)(i,i=1,neq) Write (nout,99997) t, y(1:neq) ifail = 0 Call d02nsf(neq,neq,'ANALYTIC',nwkjac,rwork,ifail) lderiv(1) = .True. lderiv(2) = .True. ifail = 0 Call d02ngf(neq,ldysav,t,tout,y,ydot,rwork,rtol,atol,itol,inform,resid, & ysav,sdysav,jac,wkjac,nwkjac,d02nby,lderiv,itask,itrace,ifail) Write (nout,99997) t, y(1:neq) 99999 Format (1X,A40,' =',1P,E8.1) 99998 Format (/1X,' t ',3X,6(' y',I1)) 99997 Format (1X,F7.4,2X,6(F8.4)) End Program d02mvfe