Numerical methods for ordinary differential equations

J.C. Butcher

440 pages, parution le 23/06/2003 (2^eme édition)

Ajouter à une liste

Indisponible

Résumé

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.

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.

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.

Differential and Difference Equations
- Differential Equation Problems
- Differential Equation Theory
- Difference Equation Problems
- Difference Equation Theory

Numerical Differential Equation Methods
- The Euler Method
- Analysis of the Euler Method
- Generalizations of the Euler Method
- Runge-Kutta Methods
- Linear Multistep Methods
- Taylor Series Methods
- Hybrid Methods

Runge-Kutta Methods
- Preliminaries
- Order Conditions
- Low Order Explicit Methods
- Runge-Kutta Methods with Error Estimates
- Implicit Runge-Kutta Methods
- Stability of Implicit Runge-Kutta Methods
- Implementable Implicit Runge-Kutta Methods
- Order Barriers
- Algebraic Properties of Runge-Kutta Methods
- Implementation Issues

Linear Multistep Methods
- Preliminaries
- The Order of Linear Multistep Methods
- Errors and Error Growth
- Stability Characteristics
- Order and Stability Barriers
- One-leg Methods and G-stability
- Implementation Issues

General Linear Methods
- Representing Methods in General Linear Form
- Consistency, Stability and Convergence
- The Stability of General Linear Methods
- The Order of General Linear Methods
- Methods with Runge-Kutta Stabiulity

References
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Wiley
Auteur(s)	J.C. Butcher
Parution	23/06/2003
Édition	2^eme édition
Nb. de pages	440
Format	15,5 x 23,5
Couverture	Relié
Poids	825g
Intérieur	Noir et Blanc
EAN13	9780471967583
ISBN13	978-0-471-96758-3