Dynamical Systems and Numerical Analysis

by Andrew Stuart, A. R. Humphries

Overview

This book unites the study of dynamical systems and numerical solution of differential equations. The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulted as dynamical systems and the convergence and stability properties of the methods are examined. Topics studied include the stability of numerical methods for contractive, dissipative, gradient and Hamiltonian systems together with the convergence properties of equilibria, periodic solutions and strage attractors under numerical approximation. This book will be an invaluable tool for graduate students and researchers in the fields of numerical analysis and dynamical systems.

Product Details

ISBN-13:	9780521496728
Publisher:	Cambridge University Press
Publication date:	08/13/1996
Series:	Cambridge Monographs on Applied and Computational Mathematics , #2
Pages:	710
Product dimensions:	6.22(w) x 9.25(h) x 1.54(d)

Table of Contents

1. Finite dimensional maps; 2. Ordinary differential equations; 3. Numerical methods for initial value problems; 4. Numerical methods as dynamical systems; 5. Global stability; 6. Convergence of invariant sets; 7. Global properties and attractors under discretisation; 8. Hamiltonian and conservative systems; Appendices; Bibliography; Index.

Editorial Reviews

"...it is clearly written and fairly self-contained, surveying two fields that have seen quite a bit of excitement in the recent past. One invaluable feature of this scholarly treatise is the bibliographical discussions at the end of each chapter, which are collected at the end of the book in an impressive list of 386 items. Also, the text is peppered with examples and exercises that are quite helpful in promoting understanding." American Scientist

"There is no doubt that the book of Stuart and Humphries constitutes a comprehensive and well-written...treatise on the deep connections between the disciplines of dynamical systems and numerical analysis. As the authors themselves state, it is primarily designed to address the needs of a researcher. However, I do believe that students with a healthy theoretical inclination and a strong mathematical background will find plenty of interesting items in this monograph...this book makes a significant contribution to both fields appearing in the title and is therefore unique and likely to remain popular for a long time." Media News & Reviews

From the Publisher

A guide to the theory of dynamical systems and the numerical solution of initial-value problems crucial to interpreting data obtained from modeling simulations and to facilitate the design of algorithms. After an introduction to theory, Stuart (Stanford U.) and Humphries (Sussex U.) formulate numerical methods as dynamical systems, examining the stability of numerical methods for contractive, dissipative, gradient,and Hamiltonian systems, and the convergence properties of equilibria, phase portraits, period solutions, and strange attractors under numerical approximation. Annotation c. by Book News, Inc., Portland, Or.

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