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Adaptive Nyström-Runge-Kutta-Methoden für gewöhnliche Differentialgleichungssysteme zweiter Ordnung

Adaptive Nyström-Runge-Kutta-Methods for systems of second-order ordinary differential equations

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Zusammenfassung

Für Differentialgleichungen zweiter Ordnung ohne erste Ableitungen wird eine Klasse verallgemeinerter Nyström-Verfahren hergeleitet. Diese Verfahren beruhen auf einer lokalen Linearisierung des Differentialgleichungssystems. Die linear impliziten Verfahren haben bei geeigneter Wahl der Stabilitätsmatrix ein unendliches Stabilitätsintervall. Sie eignen sich für die Integration von großen Systemen gewöhnlicher Differentialgleichungen, die durch Semi-Diskretisierung aus hyperbolischen Differentialgleichungen zweiter Ordnung entstehen.

Abstract

A class of generalized Nyström-methods is derived for second order differential equations without first derivatives. These methods are based on local linearization of the system of differential equations. An infinite interval of stability for linear implicit methods is achieved by appropriate choice of the stability matrix. The linear implicit methods are suitable for the integration of large systems of ordinary differential equations resulting from the semi-discretization of hyperbolic differential equations of second order.

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Authors and Affiliations

  1. Sektion Mathematik, Martin-Luther-Universität Halle-Wittenberg, Weinbergweg 17, DDR-4020, Halle a. d. Saale, Deutsche Demokratische Republik

    K. Strehmel &  R. Weiner

Authors
  1. K. Strehmel
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  2. R. Weiner
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Strehmel, K., Weiner, R. Adaptive Nyström-Runge-Kutta-Methoden für gewöhnliche Differentialgleichungssysteme zweiter Ordnung. Computing 30, 35–47 (1983). https://doi.org/10.1007/BF02253294

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  • DOI: https://doi.org/10.1007/BF02253294