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A note on stability investigations for Rosenbrock-type methods for quasilinear-implicit differential equations

Über Stabilitätsuntersuchungen von Rosenbrock-Typ-Methoden für quasilinear-implizite Differentialgleichungen

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Abstract

The solution of quasilinear-implicit ODEs using Rosenbrock type methods may suffer from stability problems despite stability properties such as A-stability or L-stability, respectively. These problems are caused by inexact computation of artificial introduced components (transformation to DAE system). The paper investigates the source of the numerical difficulties and shows modifications to overcome them.

Zusammenfassung

Bei der Lösung quasilinear-impliziter ODEs mittels Rosenbrock-Typ-Methoden können trotz guter Stabilitätseigenschaften (A- bzw. L-Stabilität) des Grundverfahrens Stabilitätsprobleme auftreten. Diese Schwierigkeiten sind auf Ungenauigkeiten bei der Berechnung künstlich eingeführter Komponenten (Überführung in DAEs) zurückzuführen. Die Arbeit untersucht die Ursachen für diese Effekte und zeigt Möglichkeiten, diese zu überwinden.

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Authors and Affiliations

  1. Institut für Numerische Mathematik Fachbereich Mathematik und Informatik, Martin-Luther-Universität Halle-Wittenberg, D-06009, Halle, Federal Republic of Germany

    M. Büttner, R. Weiner & K. Strehmel

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  1. M. Büttner
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  2. R. Weiner
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  3. K. Strehmel
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Büttner, M., Weiner, R. & Strehmel, K. A note on stability investigations for Rosenbrock-type methods for quasilinear-implicit differential equations. Computing 56, 47–59 (1996). https://doi.org/10.1007/BF02238291

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  • DOI: https://doi.org/10.1007/BF02238291

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