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.
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