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.
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Editorial Reviews
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"...it is clearly written and fairly self-contained, surveying two fields that have seen quite a bit of excitement in the recent past. One invaluable feature of this scholarly treatise is the bibliographical discussions at the end of each chapter, which are collected at the end of the book in an impressive list of 386 items. Also, the text is peppered with examples and exercises that are quite helpful in promoting understanding." American Scientist
"There is no doubt that the book of Stuart and Humphries constitutes a comprehensive and well-written...treatise on the deep connections between the disciplines of dynamical systems and numerical analysis. As the authors themselves state, it is primarily designed to address the needs of a researcher. However, I do believe that students with a healthy theoretical inclination and a strong mathematical background will find plenty of interesting items in this monograph...this book makes a significant contribution to both fields appearing in the title and is therefore unique and likely to remain popular for a long time." Media News & Reviews
"There is no doubt that the book of Stuart and Humphries constitutes a comprehensive and well-written...treatise on the deep connections between the disciplines of dynamical systems and numerical analysis. As the authors themselves state, it is primarily designed to address the needs of a researcher. However, I do believe that students with a healthy theoretical inclination and a strong mathematical background will find plenty of interesting items in this monograph...this book makes a significant contribution to both fields appearing in the title and is therefore unique and likely to remain popular for a long time." Media News & Reviews
Book Description
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.
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Inside This Book
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First Sentence:
In this chapter we introduce the theory of dynamical systems in the context of mappings in R. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof See Exercise, Proof Consider, Proof First, Remark Note, Proof Note, Proof Recall, Locally Lipschitz Problems Let, Proof By Theorem, Remark Notice, Example Let, Gauss Runge-Kutta, Hartman-Grobman Theorem, Proof Suppose, Gradient Problems Let, Hqp Hqq, Proof By Lemma, Proof Theorem, Finite Dimensional Maps, Proof Again, Remark Recall New!
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In this chapter we introduce the theory of dynamical systems in the context of mappings in R. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof See Exercise, Proof Consider, Proof First, Remark Note, Proof Note, Proof Recall, Locally Lipschitz Problems Let, Proof By Theorem, Remark Notice, Example Let, Gauss Runge-Kutta, Hartman-Grobman Theorem, Proof Suppose, Gradient Problems Let, Hqp Hqq, Proof By Lemma, Proof Theorem, Finite Dimensional Maps, Proof Again, Remark Recall New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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This book cites 34
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39
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- Numerical Analysis 1999 (Chapman & Hall/CRC Research Notes in Mathematics Series) by G.A. Watson on 6 pages
- Numerical Methods (Colloquia Mathematica Societatis Janos Bolyai) by D. Greenspan in Back Matter (1), and Back Matter (2)
- Differential Equations (with CD-ROM) by Paul Blanchard in Back Matter (1), and Back Matter (2)
- Ordinary Differential Equations (Universitext) by Vladimir I. Arnold in Back Matter
- Stability of Dynamical Systems (CBMS-NSF Regional Conference Series in Applied Mathematics) by J. P. LaSalle in Back Matter
See all 34 books this book cites
- Collocation Methods for Volterra Integral and Related Functional Differential Equations (Cambridge Monographs on Applied and Computational Mathematics) by Hermann Brunner in Front Matter, and Back Matter
- Foundations of Computational Mathematics (London Mathematical Society Lecture Note Series) by Ronald Devore on page 174, and page 343
- Radial Basis Functions: Theory and Implementations (Cambridge Monographs on Applied and Computational Mathematics) by Martin D. Buhmann in Front Matter
- Applications of Nonstandard Finite Difference Schemes by Ronald E. Mickens in Back Matter
- Generalized Riemann Problems in Computational Fluid Dynamics (Cambridge Monographs on Applied and Computational Mathematics) by Matania Ben-Artzi in Front Matter
See all 39 books citing this book
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