The Numerical Treatment of Differential Equations
VI methods are, however, immediately applicable also to non-linear prob lems, though clearly heavier computation is only to be expected; nevertheless, it is my belief that there will be a great increase in the importance of non-linear problems in the fut
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EN MATHEMATISCHEN MATHEMATISCH EN WISSENSCHAFTEN WISSENSCHAFT IN EINZELDARSTELLUNGEN MIT BESONDERER BERUCKSICHTIGUNG DER ANWENDUNGSGEBIETE HERAUSGEGEBEN VON
DOOB·· E. HEINZ HEINZ·· F. HIRZEBRUCH J. L. DOOB HOPF·· H. HOPF HOPF·· W. MAAK MAAK·· S. MAC LANE E. HOPF W. MAGNUS. MAGNUS· F. K. SCHMIDT SCHMIDT·· K. STEIN GESCHAFTSFUHRENDE HERAUSGEBER GESCHÄFTSFUHRENDE
B.ECKMANN
UND
B. L.VAN DER WAERDEN ZURICH
BAND 60
SPRINGER-VERLAG BERLIN HEIDELBERG GMBH 1966
NT NUMERICAL TREATMENT AL TREATME THE NUMERIC NS DIFFERENTIAL EQUATIONS TIAL EQUATIO OF DIFFEREN BY BY
LOIHAR COLLATZ COLLAIZ DR. LOTHAR O. PROFESSOR PROFESSOR IN IN THE THE UNIVERSITY UNIVERSITY OF OF HAMBURG HAMBURG 0.
2ND PRINTING OF THE 3RD EDITION
TRANSLATED FROM A SUPPLEMENTED VERSION OF THE SECOND GERMAN EDITION
Sc. BY P.G. WILLIAMS, B. SC.
MATHEMATICS DIVISION. NATIONAL PHYSICAL LABORATORY. TEDDINGTON. ENGLAND
WITH 118 DIAGRAMS AND 1 PORTRAIT
SPRINGER-VERLAG SPRINGER-VERLAG GMBH BERLIN HEIDELBERG GMBH BERLIN HEIDELBERG 1966 1966
Geschăftsfiihrende
Herausgeber:
Prof. Dr. B. Eckmann Eidgeniissische Technische Hochschule Ziirich
Prof. Dr. B. L. van der Waerden Mathematisches Institut der
Universităt
Ziirich
ISBN 978-3-662-05456-7 ISBN 978-3-662-05500-7 (eBook) DOI 10.1007/978-3-662-05500-7
This work is subject to copyright. Ali 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 ofthe German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the arnount ofthe fee tobe determined by agreement with the publisher. © by Springer-Verlag Berlin Heidelberg 1951, 1955, 1960 Originally published by Springer-Verlag Berlin Heidelberg New York in 1960 Softcover reprint of the hardcover 3rd edition 1960 Library of Congress Catalog Card Number 65-28340. Offsetprinting: J. Beltz, Hemsbach/Bergstr.
Collatz, Numerical treatment 3rd edition, 2nd printing
Springer-Verlag Berlin ·' Heidelberg' Heidelberg · New York
From the preface to the first edition This book constitutes an attempt to present in a connected fashion some of the most important numerical methods for the solution of ordinary and partial differential equations. The field to be covered is extremely wide, and it is clear that the present treatment cannot be remotely exhaustive; in particular, for partial differential equations it has only been possible to present the basic ideas, and many of the methods developed extensively by workers in applied fields - hydrodynamics, aerodynamics, etc. -, most of which have been developed for specific problems, have had to be dismissed with little more than a badtobe reference to the literature. However, the aim of the book is not so much to reproduce these special methods, their corresponding computing schemes, etc., as to acquaint a wide circle of engineers, physicists and mathematicians with the general
