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Boundary-value problems in partial differential equations

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The Numerical Treatment of Differential Equations

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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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  1. University of Hamburg, Hannover, Germany

    Dr. Lothar Collatz (o. Professor)

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Collatz, L. (1960). Boundary-value problems in partial differential equations. In: The Numerical Treatment of Differential Equations. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05500-7_5

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  • DOI: https://doi.org/10.1007/978-3-662-05500-7_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-05456-7

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