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Computational experiments with algorithms for stiff ODEs

Numerische Experimente mit Algorithmen für steife gewöhnliche Differentialgleichungen

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Abstract

The numerical performance of computer codes available to solve stiff systems of ODEs is evaluated. Three widely used codes of Gear/Hindmarsh, Gottwald/Wanner and Deuflhard/Bader are tested by numerous randomly generated examples which permit an arbitrary choice of the position and the number of the eigenvalues of the Jacobian. Besides a detailed evaluation of the results with regard to reliability and efficiency, examples with specified distributions of the eigenvalues and various structures of the ODEs are presented and their influence on the performance of the algorithms is discussed.

Zusammenfassung

Es wird das Leistungsvermögen von Programmen betrachtet, die für die Lösung steifer Systeme gewöhnlicher Differentialgleichungen zur Verfügung stehen. Es werden drei allgemein anwendbare Algorithmen der Autoren Gear/Hindmarsh, Gottwald/Wanner und Deuflhard/Bader durch zahlreiche zufallsmäßig erzeugte Beispiele getestet, die eine beliebige Wahl der Lage und der Zahl der Eigenwerte der Jacobi-Matrix ermöglichen. Neben einer ausführlichen Auswertung der Resultate bezüglich Zuverlässigkeit und Effektivität werden Beispiele mit speziellen Eigenwertverteilungen und unterschiedlichen Strukturen der Differentialgleichungen vorgestellt und ihr Einfluß auf die Leistungsfähigkeit der Algorithmen diskutiert.

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  1. Sektion Mathematik der Technischen Universität Dresden, Mommsenstrasse 13, DDR-8027, Dresden, German Democratic Republic

    P. Seifert

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Seifert, P. Computational experiments with algorithms for stiff ODEs. Computing 38, 163–176 (1987). https://doi.org/10.1007/BF02240180

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  • DOI: https://doi.org/10.1007/BF02240180

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