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Cambridge Monographs on Applied and Computational Mathematics : Simulating Hamiltonian Dynamics Series Number 14 - Benedict Leimkuhler

Cambridge Monographs on Applied and Computational Mathematics

Simulating Hamiltonian Dynamics Series Number 14

Hardcover

Published: 1st February 2005
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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.

'... this new book on geometric integration of Hamiltonian systems is a valuable addition to the subject that may be very useful not only as a textbook for courses in computational dynamics but also for researchers in the design of effective integrators in molecular dynamics and other areas of applied mathematics because it includes most of the recent research in the subject.' Zentralblatt MATH 'I highly recommend it for a graduate course on multivariate approximation theory, computer-aided geometric design, and meshless methods for partial differential equations.' Numerical Algorithms

Introduction
Numerical methods
Hamiltonian mechanics
Geometric integrators
The modified equations
Higher order methods
Contained mechanical systems
Rigid Body dynamics
Adaptive geometric integrators
Highly oscillatory problems
Molecular dynamics
Hamiltonian PDEs
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521772907
ISBN-10: 0521772907
Series: Cambridge Monographs on Applied and Computational Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 396
Published: 1st February 2005
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 23.5 x 16.0  x 2.3
Weight (kg): 0.75