Dynamical systems are pervasive in the modelling of naturally occurring
phenomena. Most of the models arising in practice cannot be completely
solved by anal ytic techniques; thus, numerical simulations are of funda
mental importance in gaining an understanding of dynamical systems.
It is therefore crucial to understand the behaviour of numerical sim
ulations of dynamical systems in order to interpret the data obtained
from such simulations and to facilitate the design of algorithms which
provide correct qualitative information without being unduly expensive.
These two concerns lead to the study of the convergence and stability
properties of numerical methods for dynamical systems.
The frst three chapters of this book contain the elements of the theory
of dynamical systems and the numerical solution of initial-value prob
lems. 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, phase portraits,
periodic solutions, and strange attractors under numerical approxima
tion.
This book will be an invaluable tool for graduate students and re
searchers in the felds of numerical analysis and dynamical systems.
www.cambridge.org © in this web service Cambridge University Press
Cambridge University Press
978-0-521-49672-8 - Dynamical Systems and Numerical Analysis
A. M. Stuart and A. R. Humphries
Frontmatter
More information