We are pleased to announce the publication of our new book as detailed above.
Dynamical systems are pervasive in the modelling of naturally occurring phenomena.
It is therefore crucial to 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 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 approximation.