Dynamical Systems and Numerical Analysis

This 1996 book unites the study of dynamical systems and numerical solution of differential equations.

Andrew Stuart (Author), A. R. Humphries (Author)

9780521645638, Cambridge University Press

Paperback, published 28 November 1998

712 pages
22.9 x 15.2 x 4 cm, 1.03 kg

"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

This 1996 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 formulated 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 strange 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.

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.

Subject Areas: Numerical analysis [PBKS]