I have a Nonlinear Ginzburg-Landau PDE and I have simplified it to
$$ \frac{\partial c}{\partial t} = A\left[\frac{\partial^2 c}{\partial x^2} + \frac{\partial^2 c}{\partial y^2}\right] + F(c) $$
where $A$ is a constant and $F(c)$ contains the nonlinear part of $c$ I would like to solve it using the finite difference method but I don't know where to start. is there a category for solving such equations as there is for parabolic and hyperbolic PDEs? thank
