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

Ernst Hairer

ISBN 10: 3540306633 / ISBN 13: 9783540306634

Published by Springer Berlin Heidelberg, Springer Berlin Heidelberg, 2006

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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. Seller Inventory # 9783540306634

Bibliographic Details

Title: Geometric Numerical Integration : ...

Publisher: Springer Berlin Heidelberg, Springer Berlin Heidelberg

Publication Date: 2006

Binding: Buch

Condition: Neu

Edition: 2nd Edition

About this title

Synopsis:

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.

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