The Numerical Treatment of Differential Equations

  • Lothar Collatz

Part of the Die Grundlehren der Mathematischen Wissenschaften book series (GL, volume 60)

Table of contents

About this book

Introduction

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 - hydro­ dynamics, 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 mathe­ matical 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.

Keywords

Approximation Mathematica boundary element method difference equation differential equation eigenvalue problem equation functional analysis functional equation integration interpolation ordinary differential equation partial differential equation variable wave equation

Authors and affiliations

  • Lothar Collatz
    • 1
  1. 1.HamburgGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-88434-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 1960
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-88436-8
  • Online ISBN 978-3-642-88434-4
  • Series Print ISSN 0072-7830
  • About this book