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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MATHEMATISCHEN WISSENSCHAFTEN IN EINZELDARSTELLUNGEN MIT BESONDERER BERUCKSICHTIGUNG DER ANWENDUNGSGEBIETE HERAUSGEGEBEN VON
R. GRAMMEL· F. HIRZEBRUCH· E. HOPF H. HOPF· W. MAAK· W. MAGNUS· F. K. SCHMIDT K. STEIN· B.L.VAN DER WAERDEN BAND 60
THE NUMERICAL TREATMENT OF DIFFERENTIAL EQUATIONS BY
LOTHAR COLLATZ THIRD EDITION
SPRINGER-VERLAG BERLIN· GOTTINGEN· HEIDELBERG 1960
THE NUMERICAL TREATMENT OF DIFFERENTIAL EQUATIONS BY
DR. LOTHAR COLLATZ O. PROFESSOR IN THE UNIVERSITY OF HAMBURG
THIRD EDITION
TRANSLATED FROM A SUPPLEMENTED VERSION OF THE SECOND GERMAN EDITION
BY P. G. WILLIAMS, B. SC. MATHEMATICS DIVISION, NATIONAL PHYSICAL LABORATORY, TEDDINGTON, ENGLAND
WITH 118 DIAGRAMS AND 1 PORTRAIT
SPRINGER-VERLAG BERLIN· GOTTINGEN· HEIDELBERG 1960
ISBN 978-3-642-88436-8 ISBN 978-3-642-88434-4 DOl 10.1007/978-3-642-88434-4
(eBook)
ALLE RECHTE, INSBESONDERE DAS DER "OBERSETZUNG IN FREMDE SPRACHEN VORBEHALTEN OHNE AUSDR"OCKLICHE GENEHMIGUNG DES VERLAGES 1ST ES AUCH NICHT GESTATTET, DIESES BUCH ODER TEILE DARAUS AUF PHOTOMECHANISCHEM WEGE (PHOTOKOPIE, MIKROKOPIE) ZU VERVIELFALTIGEN COPYRIGHT 1951 AND 1955 BY SPRINGER-VERLAG OHG IN BERLIN· GtlTTINGEN • HEIDELBERG
© BY SPRINGER-VERLAG OHG. BERLIN. G/:}TTINGEN • HEIDELBERG 1960 SOFTCOVER REPRINT OF THE HARDCOVER 1ST EDITION 1960
Collatz, Numerical treatment, 3rd edition
Springer-Verlag Berlin. G6ttingen . Heidelberg
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 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 methods, and to show with the aid of numerous worked examples that an idea of the quantitative behaviour of the solution of a differential equation problem can be obtained by numerical means with nothing like the trouble and labour that widespread prejudice would suggest. This prejudice may be partly due to the kind of mathematical instruction given in technical colleges and universities, in which, although the theory of differential equations is dealt with in detail, numerical methods are gone into only briefly. I have always observed that graduate mathematicians and physicists are very well acquainted with theoretical results, but have no knowledge of the simplest approximate methods. If approximate methods were more well known, perhaps many problems would be