C$TEST  TTGR6
c  main program
      common /cstak/ ds
      double precision ds(350000)
      external handle, bc, af
      integer iue, ndx, ndy, iur, ixr, iyr
      integer nxr, nyr, istkgt, i, is(1000), iu
      integer ix, iy, nu, kx, nx, ky
      integer ny, i1mach
      real abs, errpar(2), tstart, eerr, erre, errr
      real amax1, dt, lx, ly, rx, ry
      real ws(1000), rs(1000), float, tstop
      logical ls(1000)
      complex cs(500)
      integer temp, temp1, temp2
      equivalence (ds(1), cs(1), ws(1), rs(1), is(1), ls(1))
c to get error estimates for laplaces equation with real ( z*log(z) ) as
c solution.
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 = 4
      ky = 4
      ndx = 2
      ndy = 2
      tstart = 0
      tstop = 1
      dt = 1
      errpar(1) = 1e-2
      errpar(2) = 1e-4
      nx = ndx+2*(kx-1)
c space for x mesh.
      ix = istkgt(nx, 3)
      do  1 i = 1, kx
         temp = ix+i
         ws(temp-1) = 0
         temp = ix+nx-i
         ws(temp) = rx
   1     continue
c 0 and rx mult = kx.
      temp = ndx-1
      do  2 i = 1, temp
         temp2 = ix+kx-2+i
         ws(temp2) = rx*(float(i-1)/(float(ndx)-1e0))**kx
   2     continue
      ny = ndy+2*(ky-1)
c space for y mesh.
      iy = istkgt(ny, 3)
      do  3 i = 1, ky
         temp = iy+i
         ws(temp-1) = 0
         temp = iy+ny-i
         ws(temp) = ry
   3     continue
c 0 and ry mult = ky.
      temp = ndy-1
      do  4 i = 1, temp
         temp2 = iy+ky-2+i
         ws(temp2) = ry*(float(i-1)/(float(ndy)-1e0))**ky
   4     continue
c space for the solution.
      iu = istkgt(nu*(nx-kx)*(ny-ky), 3)
      call setr(nu*(nx-kx)*(ny-ky), 0e0, ws(iu))
      temp = i1mach(2)
      write (temp,  5) 
   5  format (23h solving on crude mesh.)
      call ttgr(ws(iu), nu, kx, ws(ix), nx, ky, ws(iy), ny, tstart, 
     1   tstop, dt, af, bc, errpar, handle)
      dt = 1
      ndx = 2*ndx-1
c refine mesh.
      ndy = 2*ndy-1
      nxr = ndx+2*(kx-1)
c space for x mesh.
      ixr = istkgt(nxr, 3)
      do  6 i = 1, kx
         temp = ixr+i
         ws(temp-1) = 0
         temp = ixr+nxr-i
         ws(temp) = rx
   6     continue
c 0 and rx mult = kx.
      temp = ndx-1
      do  7 i = 1, temp
         temp2 = ixr+kx-2+i
         ws(temp2) = rx*(float(i-1)/(float(ndx)-1e0))**kx
   7     continue
      nyr = ndy+2*(ky-1)
c space for y mesh.
      iyr = istkgt(nyr, 3)
      do  8 i = 1, ky
         temp = iyr+i
         ws(temp-1) = 0
         temp = iyr+nyr-i
         ws(temp) = ry
   8     continue
c 0 and ry mult = ky.
      temp = ndy-1
      do  9 i = 1, temp
         temp2 = iyr+ky-2+i
         ws(temp2) = ry*(float(i-1)/(float(ndy)-1e0))**ky
   9     continue
c space for the solution.
      iur = istkgt(nu*(nxr-kx)*(nyr-ky), 3)
      call setr(nu*(nxr-kx)*(nyr-ky), 0e0, ws(iur))
      temp = i1mach(2)
      write (temp,  10) 
  10  format (25h solving on refined mesh.)
      call ttgr(ws(iur), nu, kx, ws(ixr), nxr, ky, ws(iyr), nyr, tstart,
     1   tstop, dt, af, bc, errpar, handle)
      dt = 1
      errpar(1) = errpar(1)/10.
      errpar(2) = errpar(2)/10.
c space for the solution.
      iue = istkgt(nu*(nx-kx)*(ny-ky), 3)
      call setr(nu*(nx-kx)*(ny-ky), 0e0, ws(iue))
      temp = i1mach(2)
      write (temp,  11) 
  11  format (24h solving with errpar/10.)
      call ttgr(ws(iue), nu, kx, ws(ix), nx, ky, ws(iy), ny, tstart, 
     1   tstop, dt, af, bc, errpar, handle)
      errr = eerr(kx, ix, nx, ky, iy, ny, ws(iu), nu, ixr, nxr, iyr, 
     1   nyr, ws(iur), tstop)
      erre = 0
      temp = nu*(nx-kx)*(ny-ky)
      do  12 i = 1, temp
         temp2 = iu+i
         temp1 = iue+i
         erre = amax1(erre, abs(ws(temp2-1)-ws(temp1-1)))
  12     continue
      temp = i1mach(2)
      write (temp,  13) erre
  13  format (24h u error from u and ue =, 1pe10.2)
      temp = i1mach(2)
      write (temp,  14) errr
  14  format (24h u error from u and ur =, 1pe10.2)
      call leave
      call wrapup
      stop 
      end
      subroutine af(t, xi, nx, yi, ny, nu, u, ut, ux, uy, uxt, 
     1   uyt, a, au, aut, aux, auy, auxt, auyt, f, fu, fut, fux, fuy, 
     2   fuxt, fuyt)
      integer nu, nx, ny
      real t, xi(nx), yi(ny), u(nx, ny, nu), ut(nx, ny, nu), ux(nx, ny
     1   , nu)
      real uy(nx, ny, nu), uxt(nx, ny, nu), uyt(nx, ny, nu), a(nx, ny, 
     1   nu, 2), au(nx, ny, nu, nu, 2), aut(nx, ny, nu, nu, 2)
      real aux(nx, ny, nu, nu, 2), auy(nx, ny, nu, nu, 2), auxt(nx, ny
     1   , nu, nu, 2), auyt(nx, ny, nu, nu, 2), f(nx, ny, nu), fu(nx, 
     2   ny, nu, nu)
      real fut(nx, ny, nu, nu), fux(nx, ny, nu, nu), fuy(nx, ny, nu, nu)
     1   , 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)
               a(p, q, i, 2) = uy(p, q, i)
               aux(p, q, i, i, 1) = 1
               auy(p, q, i, i, 2) = 1
   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
      real t, x(nx), y(ny), lx, rx, ly
      real ry, u(nx, ny, nu), ut(nx, ny, nu), ux(nx, ny, nu), uy(nx, ny,
     1   nu), uxt(nx, ny, nu)
      real uyt(nx, ny, nu), b(nx, ny, nu), bu(nx, ny, nu, nu), but(nx, 
     1   ny, nu, nu), bux(nx, ny, nu, nu), buy(nx, ny, nu, nu)
      real buxt(nx, ny, nu, nu), buyt(nx, ny, nu, nu)
      integer i, j
      real cos, sin, r, alog, atan, sqrt
      real theta
      do  6 j = 1, ny
         do  5 i = 1, nx
            if (y(j) .ne. ly) goto 1
               b(i, j, 1) = uy(i, j, 1)
c neumann data on bottom.
               buy(i, j, 1, 1) = 1
               goto  4
   1           r = sqrt(x(i)**2+y(j)**2)
c dirichlet data.
               if (x(i) .le. 0.) goto 2
                  theta = atan(y(j)/x(i))
                  goto  3
   2              theta = 2.*atan(1e0)
   3           b(i, j, 1) = u(i, j, 1)-r*(cos(theta)*alog(r)-theta*sin(
     1            theta))
               bu(i, j, 1, 1) = 1
   4        continue
   5        continue
   6     continue
      return
      end
      subroutine handle(t0, u0, t, u, nv, dt, tstop)
      integer nv
      real t0, u0(nv), t, u(nv), dt, tstop
      common /a7tgrp/ errpar, nu, mxq, myq
      integer nu, mxq, myq
      real errpar(2)
      common /a7tgrm/ 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
   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
      real u(1), t
      common /cstak/ ds
      double precision ds(500)
      integer ifa, ita(2), ixa(2), nta(2), nxa(2), ixs
      integer iys, nxs, nys, istkgt, i, iewe
      integer ka(2), ma(2), is(1000), ilumd, i1mach
      real abs, erru, amax1, rs(1000), ws(1000)
      logical ls(1000)
      complex cs(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,ny-ky,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 = ilumd(ws(ix), nx, 2*kx, nxs)
c y search grid.
      iys = ilumd(ws(iy), ny, 2*ky, nys)
c u search grid values.
      iewe = istkgt(nxs*nys, 3)
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, 3)
c evaluate them.
      call tsd1(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 = amax1(erru, abs(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
      real function eerr(kx, ix, nx, ky, iy, ny, u, nu, ixr, nxr
     1   , iyr, nyr, ur, t)
      integer kx, ix, nx, ky, iy, ny
      integer nu, ixr, nxr, iyr, nyr
      real u(1), ur(1), t
      common /cstak/ ds
      double precision ds(500)
      integer ifa, ita(2), ixa(2), nta(2), nxa(2), ixs
      integer iys, nxs, nys, istkgt, i, ifar
      integer ka(2), ma(2), is(1000), ilumd, i1mach
      real abs, erru, amax1, rs(1000), ws(1000)
      logical ls(1000)
      complex cs(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 estimate at each time-step.
c u(nx-kx,ny-ky,nu), ur(nxr-kx,nyr-ky,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 / fine mesh recta
cngle.
c x search grid.
      ixs = ilumd(ws(ixr), nxr, 2*kx, nxs)
c y search grid.
      iys = ilumd(ws(iyr), nyr, 2*ky, nys)
      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, 3)
c evaluate them.
      call tsd1(2, ka, ws, ita, nta, u, ws, ixa, nxa, ma, ws(ifa))
      ka(1) = kx
      ka(2) = ky
      ita(1) = ixr
      ita(2) = iyr
      nta(1) = nxr
      nta(2) = nyr
      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.
      ifar = istkgt(nxs*nys, 3)
c evaluate them.
      call tsd1(2, ka, ws, ita, nta, ur, ws, ixa, nxa, ma, ws(ifar))
c error in solution values.
      erru = 0
      temp = nxs*nys
      do  1 i = 1, temp
         temp2 = ifar+i
         temp1 = ifa+i
         erru = amax1(erru, abs(ws(temp2-1)-ws(temp1-1)))
   1     continue
      call leave
      eerr = erru
      return
      end
      subroutine ewe(t, x, nx, y, ny, u, nu)
      integer nu, nx, ny
      real t, x(nx), y(ny), u(nx, ny, nu)
      integer i, j, p
      real cos, sin, r, alog, atan, sqrt
      real theta
c the exact solution.
      do  7 p = 1, nu
         do  6 i = 1, nx
            do  5 j = 1, ny
               r = sqrt(x(i)**2+y(j)**2)
               if (x(i) .le. 0.) goto 1
                  theta = atan(y(j)/x(i))
                  goto  2
   1              theta = 2.*atan(1e0)
   2           if (r .le. 0.) goto 3
                  u(i, j, p) = r*(cos(theta)*alog(r)-theta*sin(theta))
                  goto  4
   3              u(i, j, p) = 0
   4           continue
   5           continue
   6        continue
   7     continue
      return
      end
