A concise introduction to numerical methodsand the mathematical framework neededto understand their performance

"Numerical Solution of Ordinary Differential Equations" presents a complete and easy-to-follow introduction to classical topics in the numerical solution of ordinary differential equations. The book's approach not only explains the presented mathematics, but also helps readers understand how these numerical methods are used to solve real-world problems.

Unifying perspectives are provided throughout the text, bringing together and categorizing different types of problems in order to help readers comprehend the applications of ordinary differential equations. In addition, the authors' collective academic experience ensures a coherent and accessible discussion of key topics, including:

Euler's method

Taylor and Runge-Kutta methods

General error analysis for multi-step methods

Stiff differential equations

Differential algebraic equations

Two-point boundary value problems

Volterra integral equations

Each chapter features problem sets that enable readers to test and build their knowledge of the presented methods, and a related Web site features MATLAB(R) programs that facilitate the exploration of numerical methods in greater depth. Detailed references outline additional literature on both analytical and numerical aspects of ordinary differential equations for further exploration of individual topics.

"Numerical Solution of Ordinary Differential Equations" is an excellent textbook for courses on the numerical solution of differential equations at the upper-undergraduate and beginning graduate levels. It also serves as a valuable reference for researchers in the fields of mathematics and engineering.

The core of scientific computing is designing, writing, testing, debugging and modifying numerical software for application to a vast range of areas: from graphics, meteorology and chemistry to engineering, biology and finance. Scientists, engineers and computer scientists need to write good code, for speed, clarity, flexibility and ease of re-use. Oliveira and Stewart's style guide for numerical software points out good practices to follow, and pitfalls to avoid. By following their advice, readers will learn how to write efficient software, and how to test it for bugs, accuracy and performance. Techniques are explained with a variety of programming languages, and illustrated with two extensive design examples, one in Fortran 90 and one in C++: other examples in C, C++, Fortran 90 and Java are scattered throughout the book. This manual of scientific computing style will be an essential addition to the bookshelf and lab of everyone who writes numerical software.