Dynamical Systems and Numerical Analysis

A. M. Stuart, A.R. Humphries - Collection Cambridge Monographs on Applied and Computational Mahematics

684 pages, parution le 27/09/2004

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Résumé

Dynamical Systems are pervasive in the modelling of naturally occurring phenomena. Most of the models arising in practice cannot be completely solved by analytic techniques; thus, numerical simulations are of fundamental importance in gaining an understanding of dynamical Systems. It is therefore crucial to understand the behavior of numerical simulations of dynamical Systems in order to interpret the data obtained from such simulations and to facilitate the design of algorithms which provide correct qualitative information without being unduly expensive. These two concerns lead to the study of the convergence and stability properties of numerical methods for dynamical Systems.

The first three chapters of this book 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, phase portraits, 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.

Sommaire

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

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	A. M. Stuart, A.R. Humphries
Collection	Cambridge Monographs on Applied and Computational Mahematics
Parution	27/09/2004
Nb. de pages	684
Format	15 x 23
Couverture	Broché
Poids	947g
Intérieur	Noir et Blanc
EAN13	9780521645638
ISBN13	978-0-521-64563-8