In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This book is a fully revised update of the author's classic 1987 text, Numerical Analysis of Ordinary Differential Equations, and includes more material on linear multistep methods, whilst maintaining its emphasis on Runge-Kutta methods. It contains introductory material on differential and difference equations, and a comprehensive review of numerical methods and their potential applications. The review starts from the Euler method applied to simple problems and builds on these ideas to introduce increasingly complex methods and problems. The author then explores Runge-Kutta, linear multistep and general linear methods in detail.

• Provides a comprehensive introduction to numerical methods for solving ordinary differential equations.
• Features introductory material on differential and difference equations.
• Includes detailed coverage of Runge-Kutta, linear multistep, and general linear methods.
• Contains exercises integrated into each chapter, enabling use as a course text or for self-study.
  * Balances informal discussion with a rigorous mathematical style.
• Written by a leading authority on numerical methods.

Researchers and students from numerical methods, engineering and other sciences will find this book provides an accessible and self-contained introduction to numerical methods for solving ordinary differential equations. It stands out amongst other books on the subject because of the author's lucid writing style, and the integrated presentation of theory, examples, and exercises.