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Created March 28, 2012 18:21
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Needs["DifferentialEquations`InterpolatingFunctionAnatomy`"];
{xMin, xMax} = {-Pi/0.0677, Pi/0.0677};
k = 0.0677;
TMax = 1650;
uSolpbc[t_, x_] = u[t, x] /.
NDSolve[{D[u[t, x], t] == -100*D[u[t, x]^3*D[u[t, x], x, x, x], x] +
(1/3)*D[u[t, x]^3*D[u[t, x], x], x] -
5*D[(u[t, x]/(1 + u[t, x]))^2*D[u[t, x], x], x],
u[0, x] == 1 - 0.1*Cos[k*x], u[t, xMin] == u[t, xMax],
Derivative[0, 1]*u[t, xMin] == Derivative[0, 1]*u[t, xMax],
Derivative[0, 2]*u[t, xMin] == Derivative[0, 2]*u[t, xMax],
Derivative[0, 3]*u[t, xMin] == Derivative[0, 3]*u[t, xMax]}, u,
{t, 0, TMax}, {x, xMin, xMax}, Method ->
{"BDF", "MaxDifferenceOrder" -> 5}, MaxStepFraction -> 1/150][[1]]
NIntegrate[uSolpbc[0.1 TMax,x],{x,xMin,xMax}]
NIntegrate[uSolpbc[0.5 TMax,x],{x,xMin,xMax}]
NIntegrate[uSolpbc[0.81TMax,x],{x,xMin,xMax}]
NIntegrate[uSolpbc[ 0.88TMax,x],{x,xMin,xMax}]
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