The GPL-Stability of Runge-Kutta Methods for Delay Differential Systems

The GPL-Stability of Runge-Kutta Methods for Delay Differential Systems

Year:    2000

Journal of Computational Mathematics, Vol. 18 (2000), Iss. 1 : pp. 75–82

Abstract

This paper deals with the GPL-stability of the Implicit Runge-Kutta methods for the numerical solutions of the systems of delay differential equations. We focus on the stability behaviour of the Implicit Runge-Kutta (IRK) methods in the solutions of the following test systems with a delay term$$y'(t) = Ly(t) + My(t-\tau), t\ge 0,$$ $$y(t)=\Phi(t), t\le 0,$$where $L, M$ are $N \times N$ complex matrices, $\tau \gt 0$, $\Phi(t)$ is a given vector function. We shall show that the IRK methods are GPL-stable if and only if it is L-stable, when we use the IRK methods to the test systems above.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2000-JCM-9024

Journal of Computational Mathematics, Vol. 18 (2000), Iss. 1 : pp. 75–82

Published online:    2000-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    8

Keywords:    Delay differential equation Implicit Runge-Kutta methods GPL-stability.