دانلود کتاب Dynamical Systems and Numerical Analysis

Dynamical systems are pervasive in the modelling of naturally occurring phenomena. Most of the models arising in practice cannot be completely solved by analytic techniques; thus, numerical simulations are of fundamental importance in gaining an understanding of dynamical systems. It is therefore crucial lo understand the behaviour of numerical simulations 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 first three chapters of this book 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 ihe 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 approximation. This book will be an invaluable tool tor graduate students and researchers in the fields of numerical analysis and dynamical systems.