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Volume 18, Issue 1
The GPL-Stability of Runge-Kutta Methods for Delay Differential Systems

Biao Yang, Lin Qiu & Jiao-Xun Kuang

J. Comp. Math., 18 (2000), pp. 75-82.

Published online: 2000-02

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  • 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.

  • Keywords

Delay differential equation, Implicit Runge-Kutta methods, GPL-stability.

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  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-18-75, author = {Biao Yang, Lin Qiu and Jiao-Xun Kuang}, title = {The GPL-Stability of Runge-Kutta Methods for Delay Differential Systems}, journal = {Journal of Computational Mathematics}, year = {2000}, volume = {18}, number = {1}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9024.html} }
TY - JOUR T1 - The GPL-Stability of Runge-Kutta Methods for Delay Differential Systems AU - Biao Yang, Lin Qiu & Jiao-Xun Kuang JO - Journal of Computational Mathematics VL - 1 SP - 75 EP - 82 PY - 2000 DA - 2000/02 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9024.html KW - Delay differential equation, Implicit Runge-Kutta methods, GPL-stability. AB -

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.

Biao Yang, Lin Qiu and Jiao-Xun Kuang. (2000). The GPL-Stability of Runge-Kutta Methods for Delay Differential Systems. Journal of Computational Mathematics. 18 (1). 75-82. doi:
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