Dynamical systems and numerical analysis
著者
書誌事項
Dynamical systems and numerical analysis
（Cambridge monographs on applied and computational mathematics, 2）
Cambridge University Press, 1998
- : pbk
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注記
Originally published: 1996
Includes bibliographical references (p. 660-679) and index
内容説明・目次
内容説明
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.
目次
- 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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