Iterative solutions to classical second-order ordinary differential equations

Abstract

An elementary scheme is detailed for introducing certain basic concepts in the solution of (especially) the basic second-order ordinary differential equations of classical mathematical physics. The method proposed, an integration/iteration process, allows the development of (generally Frobenius) power series, as well as exposing the rudiments of the Green function approach to solving linear ordinary differential equations. The method assumes only a background knowledge compatible with most introductory calculus courses. Mathematics Subject Classification: 33C05, 33C15, 33C45, 34-01, 34-04, 34A25