Geometric Numerical Integration

Structure-Preserving Algorithms for Ordinary Differential Equations

Ernst Hairer, Gerhard Wanner, Christian Lubich

516 pages, parution le 17/04/2002

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Résumé

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.

Contents

Examples and Numerical Experiments
Numerical Integrators
Order Conditions, Trees and B-Series
Conservation of First Integrals and Methods on Manifolds
Symmetric Integration and Reversibility
Symplectic Integration of Hamiltonian Systems
Further Topics in Structure Preservation
Structure-Preserving Implementation
Backward Error Analysis and Structure Preservation
Hamiltonian Perturbation Theory and Symplectic Integrators
Reversible Perturbation Theory and Symmetric Integrators
Dissipatively Perturbed Hamiltonian and Reversible Systems
Highly Oscillatory Differential Equations
Dynamics of Multistep Methods

Bibliography
Index

L'auteur - Gerhard Wanner

Gerhard Wanner is the former President of Section VII of the Swiss Academy of Natural Sciences, former Head of Department of Mathematics at the University of Geneva, and former President of the Swiss Mathematical Society. He is the author of several books with Springer, including Analysis by its History, written together with Ernst Hairer.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Ernst Hairer, Gerhard Wanner, Christian Lubich
Parution	17/04/2002
Nb. de pages	516
Format	16 x 24
Couverture	Relié
Poids	872g
Intérieur	Noir et Blanc
EAN13	9783540430032