Ordinary Differential Equations

From MathsDept

by John Butcher

Butcher, J. C. 2008, WileyBlackwell, 20 March 2008, 486 pages., Hardcover # ISBN-13: 978-0470723357, ISBN-10: 0470723351

About the book (From the Editor)

The highly visual nature of the subject is accented with over 200 illustrations (8 pages of which are in color), that provide vivid representations of the cellular automata under discussion. Readers can create their own cellular automata using Java(tm) applets and simple computer code, which are available via the book's FTP site. This book serves as a valuable resource for undergraduate and graduate students and would be of interest to any reader with a scientific background. Authored by one of the world's leading authorities on numerical methods this update of one of the standard references on numerical analysis, outlines recent developments in the field and presenting a detailed overview of the area. The only book to provide both a detailed treatment of Runge-Kutta methods and a thorough exposition of general linear methods, it also provides practical guidance on solving equations associated with general linear methods, thus providing assistance to those who wish to develop their own computer code.

• Accompanied by a website hosting solutions to problems and slides for use in teaching
• Illustrated throughout by worked examples of key algorithms.
• Presents practical guidance on solving equations associated with general linear methods
• Gives an introductory overview of the field before going on to describe recent developments.
• All methods are illustrated with detailed examples and problems sets.

Synopsis

Authored by one of the world's leading authorities on numerical methods this update of one of the standard references on numerical analysis, outlines recent developments in the field and presenting a detailed overview of the area. The only book to provide both a detailed treatment of Runge-Kutta methods and a thorough exposition of general linear methods, it also provides practical guidance on solving equations associated with general linear methods, thus providing assistance to those who wish to develop their own computer code. It is accompanied by a website hosting solutions to problems and slides for use in teaching. It is illustrated throughout by worked examples of key algorithms. It presents practical guidance on solving equations associated with general linear methods. It gives an introductory overview of the field before going on to describe recent developments. All methods are illustrated with detailed examples and problems sets.

From the Back Cover

In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This second edition of the author's pioneering text is fully revised and updated to acknowledge many of these developments. It includes a complete treatment of linear multistep methods whilst maintaining its unique and comprehensive emphasis on Runge-Kutta methods and general linear methods. Although the specialist topics are taken to an advanced level, the entry point to the volume as a whole is not especially demanding. Early chapters provide a wide-ranging introduction to differential equations and difference equations together with a survey of numerical differential equation methods, based on the fundamental Euler method with more sophisticated methods presented as generalizations of Euler. Features of the book include

• Introductory work on differential and difference equations.
• A comprehensive introduction to the theory and practice of solving ordinary differential equations numerically.
• A detailed analysis of Runge-Kutta methods and of linear multistep methods.
• A complete study of general linear methods from both theoretical and practical points of view.
• The latest results on practical general linear methods and their implementation.
• A balance between informal discussion and rigorous mathematical style.
• Examples and exercises integrated into each chapter enhancing the suitability of the book as a course text or a self-study treatise.