Is there any place that I can find a list of different PDEs and common finite difference schemes used for each? I have seen tables of finite difference coefficients such as the one here http://en.wikipedia.org/wiki/Finite_difference_coefficients, but I realize that studying convergence of a finite difference scheme is a case by case study. Simply replacing the differential operators in a PDE with any arbitrary finite difference operator will not ensure consistency or stability, let alone tell us anything about the dissipation or dispersion in the scheme. So, my question is, does anybody know of a good reference that lists PDEs (common and not-so-common) and the schemes used to solve each (with explanations of the pros and cons to each scheme)?
I'd like to save some work in the future by having a good reference around.