Dynamical Systems and Numerical Analysis

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Overview

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 formulated as dynamical systems and the convergence and stability properties of the methods are examined.
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Editorial Reviews

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"...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

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Product Details

Table of Contents

Preface
Acknowledgements
1 Finite Dimensional Maps 1
2 Ordinary Differential Equations 100
3 Numerical Methods for Initial Value Problems 212
4 Numerical Methods as Dynamical Systems 269
5 Global Stability 355
6 Convergence of Invariant Sets 428
7 Global Properties and Attractors Under Discretization 497
8 Hamiltonian and Conservative Systems 574
App. A Notation 645
App. B Linear Algebra 647
App. C Fixed Point Theorems 656
Bibliography 660
Index 680
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