Geometric Numerical Integration Structure-Preserving Algorithms for
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 n
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Ernst Hairer Christian Lubich Gerhard Wanner
Geometric Numerical Integration Structure-Preserving Algorithms for Ordinary Differential Equations
With 119 Figures
~ Springer
Ernst Hairer Gerhard Wanner Universite de Geneve Section de Mathematiques C.P. 240, 2-4 rue du Lievre CH-1211 Geneve 24, Switzerland e-mail: [email protected] Gerhard. [email protected] Christian Lubich Universtitat Tiibingen Mathematisches Institut Auf der Morgenstelle 10 72076 Tiibingen, Germany e-mail: [email protected] Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP Einheitsaufnahme Hairer, Ernst: Geometric numerical integration: structure preserving algorithms for ordinary differential equations 1Ernst Hairer ; Christian Lubich ; Gerhard Wanner. - Berlin; Heidelberg; New York; Barcelona; Hong Kong; London; Milan; Paris; Tokyo: Springer, 2002 (Springer series in computational mathematics; 31)
Corrected second printing 2004 Mathematics Subject Classification (2000): 6SLxx, 6SPlO, 70Fxx, 34CXX ISSN 0179-3632 ISBN 978-3-662-05020-0 ISBN 978-3-662-05018-7 (eBook) DOl 10.1007/978-3-662-05018-7 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-Verlag Berlin Heidelberg 2002 Originally published by Springer-Verlag Berlin Heidelberg New York in 2002. Softcover reprint of the hardcover 1st edition 2002
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Preface 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 numerical methods fo
