Numerical solution of eigenvalue problems

The purpose of this chapter is to describe two very efficient methods for solving eigenvalue problems of the type encountered in linear and energy stability convection problems. The techniques referred to are the compound matrix method, which is simple to implement, and the Chebyshev tau technique. The chapter is intended to be a practical guide as to how to solve relevant eigenvalue problems. Several examples from fluid mechanics and porous convection are included. First we briefly describe a standard shooting method.