Solving Partial Differential Equations

Abstract

The simulation of partial differential equations (or PDEs) is considerably more involved than for ODEs, and much of the literature concentrates on practically important special cases. This chapter, which is no exception, just scratches the surface of PDE simulation. The methods for solving PDEs depend, among other things, on whether they are linear or not, on their degree, and on the type of boundary conditions being considered. Second-order linear PDEs are important enough to receive a classification of their own, which is recalled. The basic principles, advantages, and drawbacks of finite-difference and finite-element methods are explained, and their understanding is facilitated by the fact that the same methods have been applied to ODEs in the previous chapter.