Solving Ordinary Differential Equations II Stiff and Differential-Al
"Whatever regrets may be, we have done our best." (Sir Ernest Shackleton, turning back on 9 January 1909 at 88°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
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Editorial Board
R. L. Graham, Murray Hili J. Stoer, Würzburg R. Varga, Kent (Ohio)
E. Hairer G. Wanner
Solving Ordinary Differential Equations 11 Stift and Difterential-Algebraic Problems With 129 Figures
Springer-Verlag Berlin Heidelberg GmbH
Ernst Hairer Gerhard Wanner Universite de Geneve Sectien de Mathematiques, C.P. 240 2-4 rue du Lievre CH-1211 Geneve 24
Mathematics Subject Classificatien (1980): 65L05, 65L20, 34A50 ISBN 978-3-662-09949-0 ISBN 978-3-662-09947-6 (eBook) DOI 10.1007/978-3-662-09947-6 This work is subject ta copyri9ht. AII rights are reserved, whether the whole ar part of the material is concerned, specifically the rights of translation, reprinting, reuse of iIIustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication ofthis publication ar parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its current version, and a copyright fee must always be paid. Violations fali under the prosecution act of the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1991 Originally published by Springer-Verlag Berlin Heidelberg New York in 1991 Softcover reprint of the hardcover 1st edition 1991
41/3140-543210
This book is dedicated to the memory of Professor Peter Henrici (1923 - 1987)
His dassical text-book of 1962 on our subject "has served as a lighthousej it has established a dear framework of concepts and many fundamental results" (quoted from Stetter 1973).
Preface "Whatever regrets may be, we have done our best." (Sir Ernest Shackleton, turning back on 9 January 1909 at 88°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 (RungeKutta) methods for stiff problems, Chapter Von 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 exhibit numerical results. Investigations of a more theoretieal nature are presented in the later sections of each chapter. As in Volume I, the formulas, theorems, tables and figures are numbered consecutively in each section and indicate, in addition, the section number. In cross references to other chapters the (latin) chapter number is put first. References to the bibliography are again by "author" plus "year" in parentheses. The bibliography again contains only those papers which are discussed in the text and is in no way meant to be complete. It is a pleasure to thank J. Butcher, G. Dahlquist, and S.P. N!1Srsett (coauthor of Volume I) for their interest in the subject and for the nwnerous discussions we had with them which greatly inspired our work. Special thanks go to the par
