Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations

by Ernst Hairer, Christian Lubich, Gerhard Wanner

This book covers numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. It presents a theory of symplectic and symmetric methods, which include various specially designed integrators, as well as discusses their construction and practical merits. The long-time behavior of the numerical solutions is studied using a backward error analysis combined with KAM theory.

Genres: Mathematics

660 pages, Hardcover

First published January 1, 2002

Reviews

[Chichi Lalescu · Rating 4 out of 5]

I think the title explains already what the book is about.
What I can say is that the explanations are quite clear, with plenty of graphs to get the ideas across.

Solutions of ordinary differential equations can sometimes be shown to respect global constraints. For instance the energy of a frictionless pendulum must be conserved. This book gives a very clear overview of the numerical methods that are appropriate for such ODEs, with clear explanations and plenty of examples.