Runge-Kutta and Extrapolation Methods
Numerical methods for ordinary differential equations fall naturally into two classes: those which use one starting value at each step (“one-step methods”) and those which are based on several values of the solution (“multistep methods” or “multi-value me
- PDF / 35,203,994 Bytes
- 491 Pages / 430.866 x 649.134 pts Page_size
- 6 Downloads / 195 Views
8
Editorial Board
R. L. Graham, Murray Hill J. Stoer, Wlirzburg R. Varga, Cleveland
E. Hai rer S. P. N0rsett G. Wanner
Solving Ordinary Differential Equations I Nonstiff Problems With 105 Figures
Springer-Verlag Berlin Heidelberg GmbH
Ernst Hairer Gerhard Wanner Universite de GenElVe, Section de Mathematiques, C.P. 240, CH-1211 Geneve 24, Switzerland Syvert Paul Norsett Department of Numerical Mathematics, University of Trondheim, NTH N-?034 Trondheim, Norway
Mathematics Subject Classification (1980): 34-01, 65 L 05
ISBN 978-3-662-12609-7 ISBN 978-3-662-12607-3 (eBook) DOI 10.1007/978-3-662-12607-3
This work is subject to copyright. AII rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich. © Springer-Verlag Berlin Heidelberg 1987 Originally published by Springer-Verlag Berlin Heidelberg New York in 1987 Softcover reprinl of Ihe hardcover 1si edilion 1987
2141/3150-543210
Preface "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 c.kt. 29, 1980, to Springer Verlag)
There are two volumes, one on non-stiff equations, now finished, the second on stiff equations, in preparation. The first volume has three chapters, one on classical mathematical theory, one on RungeKutta and extrapolation methods, and one on multistep methods. There is an Appendix containing some Fortran codes which we have written for our numerical examples. Each chapter is divided into sections. Numbers of formulas, theorems, tables and figures are consecutive in each section and indicate, in addition, the section number, but not the chapter number. Cross references to other chapters are rare and are stated explicitly. The end of a proof is denoted by "QED" (quod erat demonstrandum). Since this becomes somewhat ridiculous when there is no proof at all or when the proof precedes the statement of the theorem, we wrote ''NED" (nihil erat demonstrandum) in these cases. References to the Bibliography are by "Author" plus "year" in parentheses. The Bibliography makes no attempt at being complete; we have listed mainly the papers which are discussed in the text. Finally, we want to thank all those who have helped
