I am trying to solve a system of coupled nonlinear PDEs in a rectangular region with the new FEM solver in Mathematica 10. However, I come across an error stating
NDSolveValue::femnonlinear: Nonlinear coefficients are not supported in this version of NDSolve.
Is there any workaround? I find it hard to believe that this task should not be possible. Do I have to adjust the method of the solver?
Here is my complete code:
Ω = Rectangle[{0, 0}, {2, 2}];
pdes = {-Inactive[Laplacian][u[t, x, y], {x, y}] + Derivative[1, 0, 0][u][t, x, y] ==
0.6*u[t, x, y] - u[t, x, y]^3 - v[t, x, y],
-Inactive[Laplacian][v[t, x, y], {x, y}] + Derivative[1, 0, 0][v][t, x, y] ==
1.5*u[t, x, y] - 2*v[t, x, y]};
c = {
(** ic **)
u[0, x, y] == Exp[-5 ((x - 3/2)^2 + (y - 3/2)^2)],
v[0, x, y] == Exp[-5 ((x - 1/2)^2 + (y - 1/2)^2)]
(** blank bc = noflux **)
};
{usol, vsol} = NDSolveValue[{pdes, c},
{u, v},
{x, y} ∈ Ω,
{t, 0, 2 π}
];