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The Numerical Treatment of Differential Equations pp 342–466Cite as

Boundary-value problems in partial differential equations

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

Abstract

Many of the methods described for boundary-value problems in ordinary differential equations in Chapter III carry over without difficulty to partial differential equations. What has already been said in the introduction to Chapter IV about the need for more theoretical investigation and more practical experience applies particularly to boundary-value problems for partial differential equations and bears repeating here. For the solutions of these problems we do not possess existence and uniqueness theorems covering anything like the range desirable from the standpoint of technical applications; moreover, the diversity of problems which arise in applications is continually increasing. There is also an urgent need for existing approximate methods to be subjected to extensive practical tests and thorough theoretical investigations on a much larger scale than hitherto.

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Authors and Affiliations

  1. Hamburg, Germany

    Dr. Lothar Collatz (O. Professor in the University of Hamburg)

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  1. Dr. Lothar Collatz
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© 1960 Springer-Verlag OHG. Berlin · Göttingen · Heidelberg

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Collatz, L. (1960). Boundary-value problems in partial differential equations. In: The Numerical Treatment of Differential Equations. Die Grundlehren der Mathematischen Wissenschaften, vol 60. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-88434-4_5

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  • DOI: https://doi.org/10.1007/978-3-642-88434-4_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-88436-8

  • Online ISBN: 978-3-642-88434-4

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