- #1
MathematicalPhysicist
Gold Member
- 4,699
- 371
I wrote the next code:
And I get the next two errors:
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.
Code:
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:
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.