Geometric Numerical Integration
Subtitle: Structure-Preserving Algorithms for Ordinary Differential Equations (Springer Series in Computational Mathematics)
Edition: 2nd ed. edition
Publisher: Springer
Published: April 2006
Language: eng
Format: Hardcover
Number of pages: 644
ISBN-13: 9783540306634
Subjects: Numerical analysis; Number Systems; Mathematical Analysis; Mathematics; Science/Mathematics; Mathematical Physics; Hamiltonian and reversible systems; Mathematics / Number Systems; differential equations on manifolds; geometric numerical integration; symplectic and symmetric methods; Applied
Description: Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions are the subject of this book. A complete self-contained theory of symplectic and symmetric methods, which include 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. The book is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches. The second edition is substantially revised and enlarged, with many improvements in the presentation and additions concerning in particular non-canonical Hamiltonian systems, highly oscillatory mechanical systems, and the dynamics of multistep methods.