Solving Ordinary Differential Equations I Nonstiff Problems
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E. Hairer S. P. Nørsett G. Wanner
Solving Ordinary Differential Equations I Nonstiff Problems
Second Revised Edition With 135 Figures
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Ernst Hairer Gerhard Wanner Université de Genève Section de Mathématiques 2–4 rue du Lièvre 1211 Genève 4 Switzerland [email protected] [email protected]
Syvert P. Nørsett Norwegian University of Science and Technology (NTNU) Department of Mathematical Sciences 7491 Trondheim Norway [email protected]
Corrected 3rd printing 2008 ISBN 978-3-540-56670-0
e-ISBN 978-3-540-78862-1
DOI 10.1007/978-3-540-78862-1 Springer Series in Computational Mathematics ISSN 0179-3632 Library of Congress Control Number: 93007847 Mathematics Subject Classification (2000): 65Lxx, 34A50 © 1993, 1987 Springer-Verlag Berlin Heidelberg 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 to prosecution under the German Copyright Law. 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. Cover design: WMX Design GmbH, Heidelberg Typesetting: by the authors Production: LE-TEX Jelonek, Schmidt & Vöckler GbR, Leipzig Printed on acid-free paper 98765 4321 springer.com
This edition is dedicated to Professor John Butcher on the occasion of his 60th birthday
His unforgettable lectures on Runge-Kutta methods, given in June 1970 at the University of Innsbruck, introduced us to this subject which, since then, we have never ceased to love and to develop with all our humble abilities.
From the Preface to the First Edition So far as I remember, I have never seen an Author’s Preface which had any purpose but one — to furnish reasons for the publication of the Book. (Mark Twain) Gauss’ dictum, “when a building is completed no one should be able to see any trace of the scaffolding,” is often used by mathematicians as an excuse for neglecting the motivation behind their own work and the history of their field. Fortunately, the opposite sentiment is gaining strength, and numerous asides in this Essay show to which side go my sympathies. (B.B. Mandelbrot 1982) This gives us a good occasion to work out most of the book until the next year. (the Authors in a letter, dated Oct. 29, 1980, to Springer-Verlag)
There are two volumes, one on non-stiff equations, . . ., the second on stiff equations, . . . . The first volume has three chapters, one on classical mathematical theory, one on Runge-Kutta and extrapol
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