Simulating Hamiltonian Dynamics

Benedict Leimkuhler, Sebastian Reich - Collection Cambridge Monographs on Applied and Computational Mahematics

380 pages, parution le 01/04/2005

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Résumé

Geometric integrators are time-stepping methods, designed such that they exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations. In this book the authors outline the principles of geometric integration and demonstrate how they can be applied to provide efficient numerical methods for simulating conservative models. Beginning from basic principles and continuing with discussions regarding the advantageous properties of such schemes, the book introduces methods for the N-body problem, systems with holonomic constraints, and rigid bodies. More advanced topics treated include high-order and variable stepsize methods, schemes for treating problems involving multiple time-scales, and applications to molecular dynamics and partial differential equations. The emphasis is on providing a unified theoretical framework as well as a practical guide for users. The inclusion of examples, background material and exercises enhance the usefulness of the book for self-instruction or as a text for a graduate course on the subject.

Sommaire

Preface
Acknowledgments
Introduction
Numerical methods
Hamiltonian mechanics
Geometric integrators
The modified equations
Higher order methods
Contrained mechanical systems
Rigid Body dynamics
Adaptive geometric integrators
Highly oscillatory problems
Molecular dynamics
Hamiltonian PDEs

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Benedict Leimkuhler, Sebastian Reich
Collection	Cambridge Monographs on Applied and Computational Mahematics
Parution	01/04/2005
Nb. de pages	380
Format	15,5 x 23,5
Couverture	Relié
Poids	761g
Intérieur	Noir et Blanc
EAN13	9780521772907
ISBN13	978-0-521-77290-7