This new work is an introduction to the numerical solution of the initial value problem for a system of ordinary differential equations. The first three chapters are general in nature, and chapters 4 through 8 derive the basic numerical methods, prove their convergence, study their stability and consider how to implement them effectively. The book focuses on the most important methods in practice and develops them fully, uses examples throughout, and emphasizes practical problem-solving methods.
Table of Contents
The mathematical problem: discrete variable methods
The computational problem: basic methods
Convergence and stability: stability for large step sizes
Error estimation and control: stiff problems
Some mathematical tools