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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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