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Could someone else verify that an example from the Numerical Solutions to Differential Equations isn't working.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg127308] Could someone else verify that an example from the Numerical Solutions to Differential Equations isn't working.
  • From: W Craig Carter <ccarter at MIT.EDU>
  • Date: Sun, 15 Jul 2012 04:28:27 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • Delivered-to: mathgroup-newout@smc.vnet.net
  • Delivered-to: mathgroup-newsend@smc.vnet.net

I am looking at the example on page 348 of the tutorial for a numerical solution to the Sine-Gordon equation.
(http://www.wolfram.com/learningcenter/tutorialcollection/AdvancedNumericalDifferentialEquationSolvingInMathematica/).
It doesn't work for me for M8.0.4, MacBook, MacOs 10.7.4. Can someone else verify that this doesn't work?

Here is the example:

L = 10; (*the tutorial has L=-10, but I think that is a typo. In any case, the example doesn't work with + or - *)

state = First[NDSolve`ProcessEquations[{D[u[t, x, y], t, t] ==
     D[u[t, x, y], x, x] + D[u[t, x, y], y, y] - Sin[u[t, x, y]],
    u[0, x, y] == Exp[-(x^2 + y^2)],
    Derivative[1, 0, 0][u][0, x, y] == 0,
    u[t, -L, y] == u[t, L, y], u[t, x, -L] == u[t, x, L]}, u,
   t, {x, -L, L},
   {y, -L, L},
   Method -> {"MethodOfLines",
     "SpatialDiscretization" -> {"TensorProductGrid",
       "DifferenceOrder" -> "Pseudospectral"}}]]

GraphicsGrid[Partition[Table[
   NDSolve`Iterate[state, tau];
   Plot3D[
    Evaluate[
     u[tau, x, y] /.
      NDSolve`ProcessSolutions[state, "Forward"]], {x, -L, L}, {y, -L,
      L}, PlotRange -> {-1/4, 1/4}],
   {tau, 0, 20, 5}], 2]]


Thanks, Craig


W Craig Carter
Professor of Materials Science, MIT


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