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.

chapter 1|57 pages

The Mathematical Problem

chapter 2|38 pages

Discrete Variable Methods

chapter 3|42 pages

The Computational Problem

chapter 4|70 pages

Basic Methods

chapter 5|60 pages

Convergence and Stabilit

chapter 6|46 pages

Stability for Large Step Sizes

chapter 7|68 pages

Error Estimation and Control

chapter 8|46 pages

Stiff Problems