CHAPTER 3 - Ordinary Differential Equations

Abstract

This chapter focuses on ordinary differential equations. Ordinary differential equation problems of mathematical physics fall into two classes: initial value problems and boundary value problems. While it is possible to design numerical methods for initial value problems of great generality, only special boundary value problems can be treated. For both types of problems, finite difference or discrete variable methods lend themselves best to automatic digital computation. A discrete variable method is one in which an approximate solution of the differential equation is sought only at a finite number of points. Homogeneous boundary value problems commonly occur in the description of the fundamental or characteristic frequencies of vibrating strings, beams, membranes, and other structures. A simple example is the vibrating string.