Dynamical Systems and Numerical Analysis

Dynamical Systems and Numerical Analysis

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Cambridge University Press


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Dynamical Systems and Numerical Analysis

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: 9780521645638
Publisher: Cambridge University Press
Publication date: 09/28/2009
Series: Cambridge Monographs on Applied and Computational Mathematics Series , #2
Edition description: Reprint
Pages: 712
Product dimensions: 5.98(w) x 8.98(h) x 1.57(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.

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