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Problem solving highly non-linear pdes in mathematica! Can anyone help?

  1. Jul 9, 2009 #1
    I keep getting the error,
    NDSolve`FiniteDifferenceDerivative::aord: The approximation order 0 given for dimension 1 should be a positive machine-sized integer or Pseudospectral.

    I have a very complex and nonlinear pde to solve in mathematica and I keep getting errors with the code. Everything seems right to me and I can't figure out whats wrong. Is there a problem with the initial or boundary conditions? or is it not possible to solve such a complicated equation? Any help would be really appreciated! Thanks


    Here is a copy of the code I am using(with mathematica 7):


    With[{Re = 77.33},
    NDSolve[{D[q[x, t],
    t] == (10/Re)[h[x, t] - (q[x, t]/h[x, t]^2)] + (9/7)[q[x, t]^2]*
    D[h[x, t], {x, 1}]/h[x, t]^2 - (17/7) q[x, t]*
    D[q[x, t], {x, 1}]/h[x, t] + (5/6)*5*h[x, t]*
    D[h[x, t], {x, 3}] + (1/Re) [(373/28) q[x, t]*
    D[h[x, t], {x, 1}]^2/h[x, t]^2 - (205/168)*h[x, t]^2*
    D[h[x, t], {x, 2}] - (2837/168)*q[x, t]*
    D[h[x, t], {x, 2}]/h[x, t] + (449/28)*
    D[q[x, t], {x, 2}] - (339/28)*D[q[x, t], {x, 1}]*
    D[h[x, t], {x, 1}]/h[x, t] - (45/14) h[x, t]*
    D[h[x, t], {x, 1}]^2] ,
    D[h[x, t], {t, 1}] + D[q[x, t], {x, 1}] == 0,
    q[0, t] == 1 + .05 Sin[2*Pi*5 t],
    h[0, t] == (1 + .05 Sin[2*Pi*5 t])^(1/3),
    Derivative[1, 0][q][0, t] == 0,
    Derivative[1, 0][h][0, t] == cos[t], h[x, 0] == sin[x],
    q[x, 0] == sin[x]}, {q, h}, {t, .0001, 10}, {x, .0001, 10}]]
     
  2. jcsd
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