Geometric Numerical Integration

• Examples and Numerical Experiments.- Numerical Integrators.- Order Conditions, Trees and B-Series.- Conservation of First Integrals and Methods on Manifolds.- Symmetric Integration and Reversibility.- Symplectic Integration of Hamiltonian Systems.- Non-Canonical Hamiltonian Systems.- Structure-Preserving Implementation.- Backward Error Analysis and Structure Preservation.- Hamiltonian Perturbation Theory and Symplectic Integrators.- Reversible Perturbation Theory and Symmetric Integrators.- Dissipatively Perturbed Hamiltonian and Reversible Systems.- Oscillatory Differential Equations with Constant High Frequencies.- Oscillatory Differential Equations with Varying High Frequencies.- Dynamics of Multistep Methods.

From the reviews of the second edition: "This book is highly recommended for advanced courses in numerical methods for ordinary differential equations as well as a reference for researchers/developers in the field of geometric integration, differential equations in general and related subjects. It is a must for academic and industrial libraries." -- MATHEMATICAL REVIEWS "The second revised edition of the monograph is a fine work organized in fifteen chapters, updated and extended. ... The material of the book is organized in sections which are ... self-contained, so that one can dip into the book to learn a particular topic ... . A person interested in geometrical numerical integration will find this book extremely useful." (Calin Ioan Gheorghiu, Zentralblatt MATH, Vol. 1094 (20), 2006)