Geometric Numerical Integration Structure-Preserving Algorithms for
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 symm
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Geometric Numerical Integration Structure-Preserving Algorithms for Ordinary Differential Equations Second Edition
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Springer Series in Computational Mathematics
Editorial Board R. Bank R.L. Graham J. Stoer R. Varga H. Yserentant
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Ernst Hairer Christian Lubich Gerhard Wanner
Geometric Numerical Integration Structure-Preserving Algorithms for Ordinary Differential Equations Second Edition
With 146 Figures
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Ernst Hairer Gerhard Wanner
Christian Lubich Mathematisches Institut Universität Tübingen Auf der Morgenstelle 10 72076 Tübingen, Germany email: [email protected]
Section de Mathématiques Université de Genève 2-4 rue du Lièvre, C.P. 64 CH-1211 Genève 4, Switzerland email: [email protected] [email protected]
Library of Congress Control Number: 2005938386
Mathematics Subject Classification (2000): 65Lxx, 65P10, 70Fxx, 34Cxx ISSN 0179-3632 ISBN-10 3-540-30663-3 Springer Berlin Heidelberg New York ISBN-13 978-3-540-30663-4 Springer Berlin Heidelberg New York ISBN-10 3-540-43003-2 1st Edition Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2002, 2004, 2006 Printed in The Netherlands The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: by the authors and TechBooks using a Springer LATEX macro package Cover design: design & production GmbH, Heidelberg Printed on acid-free paper
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Preface to the First Edition
They throw geometry out the door, and it comes back through the window. (H.G.Forder, Auckland 1973, reading new mathematics at the age of 84)
The subject of this book is numerical methods that preserve geometric properties of the flow of a differential equation: symplectic integrators for Hamiltonian systems, symmetric integrators for reversible systems, methods preserving first integrals and numerical methods on manifolds, including Lie group methods and integrators for constrained mechanical systems, and methods for problems with highly oscillatory solutions. Structure preservation – with its questions as to where, how, and what for – is the unifying theme. In the last few decades, the theory of numeri
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