I have a nasty non-linear partial differential equation. I wonder if there exists a method that would allow me to examine what numerical errors (like numerical diffusion or dispersion) are introduced by different approximation schemes. Name of the method or a link to a paper would be great.EDIT: Equation$$\frac{\partial f}{\partial t}+\frac{\partial}{\partial x} \left(\sqrt{c-\frac{\partial f}{\partial x}} \right)=0$$$c$ is a constant.
Is there a method to examine numerical diffusion for non-linear PDE?
numerical analysis
The usual way of evaluating the accuracy of a solution scheme is to compare a numerical solution with an analytically known one. If you can't find a solution to the exact problem you have here (as is likely, given that it's nonlinear), you can always construct one using the Method of Manufactured Solutions. There are many descriptions of this method, one of which is here.