Solving Ordinary Differential Equations II Stiff and Differential-Al
The subject of this book is the solution of stiff differential equations and of differential-algebraic systems (differential equations with constraints). There is a chapter on one-step and extrapolation methods for stiff problems, another on multistep met
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Springer-Verlag Berlin Heidelberg GmbH
E. Hairer
G. Wanner
Solving Ordinary Differential Equations II Stiff and Differential-Algebraic Problems Second Revised Edition With 137 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] Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnehme Solving ordinary differential equations I E. Hairer; G. Wanner.
Bd.l verf. van E. Hairer, S.P Norsett und G. Wanner NE: Hairer, Ernst; Norsett. Syvert P.; WalU1er, Gerhard 2.
Stiff and differential algebraic problems. - 2., rev. ed. - 1996
(Springer Series in Computational mathematics; 14) ISBN 978-3-642-05220-0 ISBN 978-3-642-05221-7 (eBook) DOI 10.1007/978-3-642-05221-7
NE:GT
Corrected Second Printing 2002 The cover design of the Springer Series in Computational Mathematics is based on Figure IOA on page 149 of this book.
Mathematics Subject Classification (2000): 65Lxx, 34A50
This work is subject to copyright. AII 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 ar in any other way, and storage in data banks. Duplication of this publication ar 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-Verlag Berlin Heidelberg GmbH.
Violations are liable for prosecution under the German Copyright Law. springeronline.com © Springer-Verlag Berlin Heidelberg 1991,1996 Originally published by Springer-Verlag Berlin Heidelberg New York in 1996 Softcover reprint of the hardcover 2nd edition 1996
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: design&production, Heidelberg Camera-ready copy by the authors Printed an acid-free paper
46/3142ck-54321
To Evi and Myriam
From the Preface to the First Edition "Whatever regrets may be, we have done our best." (Sir Ernest Shackleton, turning back on 9 January 1909 at 88 0 23' South.)
Brahms struggled for 20 years to write his first symphony. Compared to this, the 10 years we have been working on these two volumes may even appear short. This second volume treats stiff differential equations and differential algebraic equations. It contains three chapters: Chapter IV on one-step (Runge-Kutta) methods for stiff problems, Chapter V on multistep methods for stiff problems, and Chapter VI on singular perturbation and differential-algebraic equations. Each chapter is divided into sections. Usually the first sections of a chapter are of an introductory nature, explain numerical phenomena and e
