Geometric Numerical Integration
Structure-Preserving Algorithms for Ordinary Differential Equations
1st Edition
Published on 9. March 2013
XIII, 515 pages
978-3-662-05018-7 (ISBN)
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.
Reviews / Votes
"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 REVIEWSMore details
Other editions
New editions
Ernst Hairer | Christian Lubich | Gerhard Wanner
Geometric Numerical Integration
Structure-Preserving Algorithms for Ordinary Differential Equations
E-Book
05/2006
2nd Edition
Springer
€223.63
Available for download
Additional editions
Ernst Hairer | Christian Lubich | Gerhard Wanner
Geometric Numerical Integration
Structure-Preserving Algorithms for Ordinary Differential Equations
Book
08/2004
Springer
€85.59
Article exhausted; check for reprint
Content
I. Examples and Numerical Experiments.- II. Numerical Integrators.- III. Order Conditions, Trees and B-Series.- IV. Conservation of First Integrals and Methods on Manifolds.- V. Symmetric Integration and Reversibility.- VI. Symplectic Integration of Hamiltonian Systems.- VII. Further Topics in Structure Preservation.- VIII. Structure-Preserving Implementation.- IX. Backward Error Analysis and Structure Preservation.- X. Hamiltonian Perturbation Theory and Symplectic Integrators.- XI Reversible Perturbation Theory and Symmetric Integrators.- XII. Dissipatively Perturbed Hamiltonian and Reversible Systems.- XIII. Highly Oscillatory Differential Equations.- XIV. Dynamics of Multistep Methods.
