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A stable explicit difference approximation of the one-dimensional diffusion equation

Ein stabiles explizites Diffrenzeverfahren zur Lösung der eindimensionalen Wärmeleitungsgleichung

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Abstract

An explicit difference approximation of the one-dimensional diffusion equation equation, which is stable for any choice of the difference gird and has a comparatively small truncation error, is described. A smoothing formula, which makes the practical use of this method possible, is given.

Zusammenfassung

Zuerst wird ein explizites Differenzenverfahren beschrieben, das die eindimensionale Wärmeleitungs-gleichung approximiert und bei willkürlicher Wahl des Differenzengitters stabil ist. Dann folgt die Beschreibung eines Glättungsverfahrens, das die praktische Anwendung dieser Methode ermöglicht.

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Authors and Affiliations

  1. Department of Computer Science, University of South Africa, P. O. Box 392, Pretoria, South Africa

    G. R. Joubert

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  1. G. R. Joubert
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Joubert, G.R. A stable explicit difference approximation of the one-dimensional diffusion equation. Computing 11, 315–325 (1973). https://doi.org/10.1007/BF02239158

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  • DOI: https://doi.org/10.1007/BF02239158

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