Dynamical systems and numerical analysis

✍ Scribed by Stuart, A. M.; Humphries, A. R

Publisher: Cambridge University Press
Year: 1998
Tongue: English
Leaves: 709
Series: Cambridge monographs on applied and computational mathematics 2
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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

✦ Table of Contents

Content: Finite dimensional maps --
Ordinary differential equations --
Numerical methods for initial value problems --
Numerical methods as dynamical systems --
Global stability --
Convergence of invariant sets --
Global properties and attractors under discretization --
Hamiltonian and conservative systems --
Appendices.

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