Description: 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.
Review Quotes: "...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