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

[christensen22]

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 what's 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}]]

 

[gtoguy97]

</code>The error is related to the finite difference approximation of the derivative you are using. Try increasing the approximation order of the derivative in your code. For example, for the first derivative of h[x,t] use D[h[x,t],{x,2}] instead of D[h[x,t],{x,1}]. That should help reduce the error.