ABSTRACT
This chapter considers the elementary and generally useful method known as separation of variables. The separation procedure reduces the partial differential equation to several ordinary differential equations. In some cases these can be solved trivially. The chapter discusses the series expansion method for second order ordinary differential equations. It explains the discussion of the eigenvalue problem by a study of Sturm-Liouville theory for second order ordinary differential equations. Numerical methods provide a useful and often unavoidable alternative to the analytic methods discussed for the solution of ordinary differential equations and eigenvalue problems. This is a big subject, and can only scratch the surface. The Runge-Kutta and other more elaborate schemes are described in detail in works on numerical methods. An important question discussed in these works is that of stability. The differential equation is approximated by a difference equation.
