C\$TEST DTTGR1 c main program common /cstak/ ds double precision ds(350000) external handle, bc, af integer ndx, ndy, istkgt, is(1000), iu, ix integer iy, nu, kx, nx, ky, ny integer idumb real errpar(2), rs(1000) logical ls(1000) complex cs(500) double precision tstart, dt, lx, ly, rx, ry double precision ws(500), tstop equivalence (ds(1), cs(1), ws(1), rs(1), is(1), ls(1)) c to solve the heat equation with solution u == t*x*y, c grad . ( u + ux + .1 * uy, u + uy + .1 * ux ) = ut + ux + uy +g(x,t) c the port library stack and its aliases. c initialize the port library stack length. call istkin(350000, 4) call enter(1) nu = 1 lx = 0 rx = 1 ly = 0 ry = 1 kx = 2 ky = 2 ndx = 3 ndy = 3 tstart = 0 tstop = 1 dt = 1 errpar(1) = 1e-2 errpar(2) = 1e-4 c uniform grid. ix = idumb(lx, rx, ndx, kx, nx) c uniform grid. iy = idumb(ly, ry, ndy, ky, ny) c space for the solution. iu = istkgt(nu*(nx-kx)*(ny-ky), 4) c initial conditions for u. call setd(nu*(nx-kx)*(ny-ky), 0d0, ws(iu)) call dttgr(ws(iu), nu, kx, ws(ix), nx, ky, ws(iy), ny, tstart, 1 tstop, dt, af, bc, errpar, handle) call leave call wrapup stop end subroutine af(t, x, nx, y, ny, nu, u, ut, ux, uy, uxt, uyt 1 , a, au, aut, aux, auy, auxt, auyt, f, fu, fut, fux, fuy, fuxt, 2 fuyt) integer nu, nx, ny double precision t, x(nx), y(ny), u(nx, ny, nu), ut(nx, ny, nu), 1 ux(nx, ny, nu) double precision uy(nx, ny, nu), uxt(nx, ny, nu), uyt(nx, ny, nu), 1 a(nx, ny, nu, 2), au(nx, ny, nu, nu, 2), aut(nx, ny, nu, nu, 2) double precision aux(nx, ny, nu, nu, 2), auy(nx, ny, nu, nu, 2), 1 auxt(nx, ny, nu, nu, 2), auyt(nx, ny, nu, nu, 2), f(nx, ny, nu) 2 , fu(nx, ny, nu, nu) double precision fut(nx, ny, nu, nu), fux(nx, ny, nu, nu), fuy(nx, 1 ny, nu, nu), fuxt(nx, ny, nu, nu), fuyt(nx, ny, nu, nu) integer i, p, q do 3 i = 1, nu do 2 q = 1, ny do 1 p = 1, nx a(p, q, i, 1) = ux(p, q, i)+.1*uy(p, q, i)+u(p, q, i) a(p, q, i, 2) = uy(p, q, i)+.1*ux(p, q, i)+u(p, q, i) aux(p, q, i, i, 1) = 1 auy(p, q, i, i, 2) = 1 auy(p, q, i, i, 1) = .1 aux(p, q, i, i, 2) = .1 au(p, q, i, i, 1) = 1 au(p, q, i, i, 2) = 1 f(p, q, i) = ut(p, q, i)+ux(p, q, i)+uy(p, q, i) fut(p, q, i, i) = 1 fux(p, q, i, i) = 1 fuy(p, q, i, i) = 1 f(p, q, i) = f(p, q, i)+.2*t-x(p)*y(q) 1 continue 2 continue 3 continue return end subroutine bc(t, x, nx, y, ny, lx, rx, ly, ry, u, ut, ux, 1 uy, uxt, uyt, nu, b, bu, but, bux, buy, buxt, buyt) integer nu, nx, ny double precision t, x(nx), y(ny), lx, rx, ly double precision ry, u(nx, ny, nu), ut(nx, ny, nu), ux(nx, ny, nu) 1 , uy(nx, ny, nu), uxt(nx, ny, nu) double precision uyt(nx, ny, nu), b(nx, ny, nu), bu(nx, ny, nu, 1 nu), but(nx, ny, nu, nu), bux(nx, ny, nu, nu), buy(nx, ny, nu 2 , nu) double precision buxt(nx, ny, nu, nu), buyt(nx, ny, nu, nu) integer i, j do 2 j = 1, ny do 1 i = 1, nx bu(i, j, 1, 1) = 1 b(i, j, 1) = u(i, j, 1)-t*x(i)*y(j) 1 continue 2 continue return end subroutine handle(t0, u0, t, u, nv, dt, tstop) integer nv double precision t0, u0(nv), t, u(nv), dt, tstop common /d7tgrp/ errpar, nu, mxq, myq integer nu, mxq, myq real errpar(2) common /d7tgrm/ kx, ix, nx, ky, iy, ny integer kx, ix, nx, ky, iy, ny if (t0 .ne. t) goto 2 write (6, 1) t 1 format (16h restart for t =, 1pe10.2) return c get and print the error. 2 call gerr(kx, ix, nx, ky, iy, ny, u, nu, t) return end subroutine gerr(kx, ix, nx, ky, iy, ny, u, nu, t) integer kx, ix, nx, ky, iy, ny integer nu double precision u(1), t common /cstak/ ds double precision ds(500) integer ifa, ita(2), ixa(2), nta(2), nxa(2), idlumd integer ixs, iys, nxs, nys, istkgt, i integer iewe, ka(2), ma(2), is(1000), i1mach real rs(1000) logical ls(1000) complex cs(500) double precision dabs, erru, dmax1, ws(500) integer temp, temp1, temp2 equivalence (ds(1), cs(1), ws(1), rs(1), is(1), ls(1)) c to get and print the error at each time-step. c u(nx-kx,ny0ky,nu). c the port library stack and its aliases. call enter(1) c find the error in the solution at 2*kx * 2*ky points / mesh rectangle. c x search grid. ixs = idlumd(ws(ix), nx, 2*kx, nxs) c y search grid. iys = idlumd(ws(iy), ny, 2*ky, nys) c u search grid values. iewe = istkgt(nxs*nys, 4) c the exact solution. call ewe(t, ws(ixs), nxs, ws(iys), nys, ws(iewe), nu) ka(1) = kx ka(2) = ky ita(1) = ix ita(2) = iy nta(1) = nx nta(2) = ny ixa(1) = ixs ixa(2) = iys nxa(1) = nxs nxa(2) = nys ma(1) = 0 c get solution. ma(2) = 0 c approximate solution values. ifa = istkgt(nxs*nys, 4) c evaluate them. call dtsd1(2, ka, ws, ita, nta, u, ws, ixa, nxa, ma, ws(ifa)) c error in solution values. erru = 0 temp = nxs*nys do 1 i = 1, temp temp2 = iewe+i temp1 = ifa+i erru = dmax1(erru, dabs(ws(temp2-1)-ws(temp1-1))) 1 continue temp = i1mach(2) write (temp, 2) t, erru 2 format (14h error in u(.,, 1pe10.2, 3h) =, 1pe10.2) call leave return end subroutine ewe(t, x, nx, y, ny, u, nu) integer nu, nx, ny double precision t, x(nx), y(ny), u(nx, ny, nu) integer i, j, p c the exact solution. do 3 p = 1, nu do 2 i = 1, nx do 1 j = 1, ny u(i, j, p) = t*x(i)*y(j) 1 continue 2 continue 3 continue return end