An edition of Geometric Numerical Integration (2002)

Geometric Numerical Integration

Structure-Preserving Algorithms for Ordinary Differential Equations

By Ernst Hairer

0 (0 Ratings)

1 Want to read0 Currently reading0 Have read

Publish Date

2002

Publisher

Springer Berlin Heidelberg

Language

eng

Pages

660

Description:

The subject of this book is numerical methods that preserve geometric properties of the flow of a differential equation: symplectic integrators for Hamiltonian systems, symmetric integrators for reversible systems, methods preserving first integrals and numerical methods on manifolds, including Lie group methods and integrators for constrained mechanical systems, and methods for problems with highly oscillatory solutions. A complete theory of symplectic and symmetric Runge-Kutta, composition, splitting, multistep and various specially designed integrators is presented, and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory and related perturbation theories. The book is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches.