Dynamical Systems and Numerical Analysis

Erscheinungsjahr 2012
ISBN: 978-0-521-49672-8
Verlag: Cambridge University Press

Buch, Englisch, Band 2, 709 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 1286 g

Reihe: Cambridge Monographs on Applied and Computational Mathematics

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 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.

Autoren/Hrsg.

Stuart, A. M.

Stuart, Andrew

Humphries, A. R.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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.