Overview

This is an essential book for the computational mathematician wanting to understand the background, motivation, and the significance of the symplectic geometric algorithm. It will be useful for numerical analysts and for those in other related disciplines.

Full Product Details

Author:   K. Feng ,  Mengzhao Qin
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Dimensions:   Width: 15.60cm , Height: 3.80cm , Length: 23.40cm
Weight:   1.155kg
ISBN:  

9783642017766

ISBN 10:   3642017762
Pages:   704
Publication Date:   December 2009
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Preliminaries of Differential Manifolds.- Symplectic Algebra and Geometry Preliminaries.- Hamiltonian Mechanics and Symplectic Geometry.- Symplectic Difference Schemes for Hamiltonian Systems.- The Generating Function Method.- The Calculus of Generating Function and Formal Energy.- Symplectic Runge-Kutta Methods.- Composition Scheme.- Formal Power Series and B-Series.- Volume-Preserving Methods for Source-Free Systems.- Free Systems.- Contact Algorithms for Contact Dynamic Systems.- Poisson Bracket and Lie-Poisson Schemes.- KAM Theorem of Symplectic Algorithms.- Lee-Variational Integrator.- Structure Preserving Schemes for Birkhoff Systems.- Multisymplectic and Variational Integrators.

Reviews

From the reviews: </p> This book is about the construction of numerical algorithms that preserve geometric properties and physical principles associated with ordinary differential systems. the book provides a comprehensive overview of geometric numerical integration of Hamiltonian systems, also offering some of the outstanding results achieved by the authors, making this monograph a valuable contribution to the bibliography in this field that will be of interest to a wide range of researchers in a variety of areas. (A. San Miguel, Mathematical Reviews, Issue 2012 h)</p>

From the reviews: This book is about the construction of numerical algorithms that preserve geometric properties and physical principles associated with ordinary differential systems. the book provides a comprehensive overview of geometric numerical integration of Hamiltonian systems, also offering some of the outstanding results achieved by the authors, making this monograph a valuable contribution to the bibliography in this field that will be of interest to a wide range of researchers in a variety of areas. (A. San Miguel, Mathematical Reviews, Issue 2012 h)

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