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A stability property ofA-stable natural Runge-Kutta methods for systems of delay differential equations

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Abstract

A natural Runge-Kutta method is a special type of Runge-Kutta method for delay differential equations (DDEs); it is known that any one-step collocation method is equivalent to one of such methods. In this paper, we consider a linear constant-coefficient system of DDEs with a constant delay, and discuss the application of natural Runge-Kutta methods to the system. We show that anA-stable method preserves the asymptotic stability property of the analytical solutions of the system.

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Authors and Affiliations

  1. Department of Computer Science and Information Mathematics, The University of Electro-Communications, 1-5-1, Chofugaoka, Chofu, 182, Tokyo, Japan

    T. Koto

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  1. T. Koto
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Koto, T. A stability property ofA-stable natural Runge-Kutta methods for systems of delay differential equations. BIT 34, 262–267 (1994). https://doi.org/10.1007/BF01955873

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  • DOI: https://doi.org/10.1007/BF01955873

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