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D-stability and Kaps-Rentrop-methods

D-Stabilität und Kaps-Rentrop-Verfahren

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Abstract

In this paper we give an analysis of the effect of stiff nonlinearities on the behavior of a Kaps-Rentrop method. To that end we introduce two quantities related to a simple model. The values of these quantities determine to some extent the behavior of a Kaps-Rentrop method in case of a strong coupling between the smooth component and the transient one. Numerical examples illustrate the theoretical results.

Zusammenfassung

In dieser Arbeit wird die Stabilität des Kaps-Rentrop-Verfahrens in die Anwesenheit nichtlinearer Steifheit (Stiffness) analysiert. Dazu werden mittels eines einfachen Modells zwei Größen introduziert. Die Werte dieser Größen reflektieren gewissermaßen das Verhalten eines Kaps-Rentrop-Verfahrens in die Anwesenheit einer bestimmten Kopplung zwischen die beiden Komponenten in das steife System gewöhnlicher Differentialgleichungen. Einige numerische Beispiele veranschaulichen die Analyse.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Vrije Universiteit, Postbus 7161, 1081 HV, Amsterdam, The Netherlands

    M. van Veldhuizen

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  1. M. van Veldhuizen
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van Veldhuizen, M. D-stability and Kaps-Rentrop-methods. Computing 32, 229–237 (1984). https://doi.org/10.1007/BF02243574

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  • DOI: https://doi.org/10.1007/BF02243574

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