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Über die Konvergenzordnung von Differenzenverfahren, die parabolische Anfangsrandwertaufgaben approximieren

On the rate of convergence of difference-schemes which approximate parabolic initial-value problems

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Zusammenfassung

Die Konvergenzordnung eines Differenzenverfahrens ist von den Differenzierbarkeitseigenschaften der Lösung der Differentialgleichung abhängig. Bei parabolischen Anfangsrandwertaufgaben werden diese durch die Anfangsfunktion bestimmt. Es wird das Verhalten der Konvergenzordnung in Abhängigkeit von der Anfangsfunktion untersucht.

Summary

The rate of convergence of a difference-scheme depends on the differentiability of the solution of the differential equation. In parabolic initial-value problems this is determined by the initial function. We examine the changing of the rate of convergence in dependence on the initial function.

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Authors and Affiliations

  1. Rechenzentrum der Universität Hamburg, Rothenbaumchaussee 81, D-2, Hamburg 13, Bundesrepublik Deutschland

    Burkhard Monien

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  1. Burkhard Monien
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Dieser Aufsatz ist Herrn Professor Dr.L. Collatz mit den besten Wünschen zu seinem 60. Geburtstag gewidmet

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Monien, B. Über die Konvergenzordnung von Differenzenverfahren, die parabolische Anfangsrandwertaufgaben approximieren. Computing 5, 221–245 (1970). https://doi.org/10.1007/BF02248023

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  • DOI: https://doi.org/10.1007/BF02248023

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