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A PDE in maple 18.

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  1. Jul 10, 2014 #1

    MathematicalPhysicist

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    Gold Member

    I wrote the next code:
    Code (Text):

    restart;
    pde := diff(u(x, t), t)+diff(u(x, t), x)-(diff(diff(u(x, t), x), t))^2 = u(x, t);
       
    tmax := 0.5e-1;
    xmin := 0;
    xmax := 1;
     N := 10;
     bc1 := du(xmin, t) = 0;
     bc2 := u(xmax, t) = 0;
     ic1 := u(x, 0) = 1;
    ic2 := du(x, 0) = 2;
     bcs := {u(x, 0) = rhs(ic1), (D[1](u))(0, t) = rhs(bc1)};

    pds := pdsolve(pde, bcs, numeric, time = t, range = 0 .. xmax, indepvars = [x, t], spacestep = (1/1000)*xmax, timestep = (1/1000)*tmax);
     
    pds:-plot3d(t = 0 .. tmax, x = xmin .. xmax, axes = boxed, orientation = [-150, 80], shading = zhue, transparency = .1)
     
    And I get the next two errors:
    Code (Text):
    Error, (in pdsolve/numeric/plot3d) unable to compute solution for t>HFloat(0.0):
    Newton iteration is not converging
    Is there a method that will converge for this PDE?

    Maybe Runga Kutta?

    Thanks in advance.

    Btw, the PDE that I had in mind is: [tex]u_x+u_t - (u_{xt})^2 = u[/tex] a nonlinear pde.
     
  2. jcsd
  3. Jul 17, 2014 #2
    I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
     
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