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Volume 22, Issue 4
Asymptotic Stability of Runge-Kutta Methods for the Pantograph Equations

Jingjun Zhao, Wanrong Cao & Mingzhu Liu

J. Comp. Math., 22 (2004), pp. 523-534.

Published online: 2004-08

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  • Abstract

This paper considers the asymptotic stability analysis of both exact and numerical solutions of the following neutral delay differential equation with pantograph delay.

image.png

where $B,C,D\in C^{d\times d},q\in (0,1)$,and $B$ is regular. After transforming the above equation to non-automatic neutral equation with constant delay, we determine sufficient conditions for the asymptotic stability of the zero solution. Furthermore, we focus on the asymptotic stability behavior of Runge-Kutta method with variable stepsize. It is proved that a L-stable Runge-Kutta method can preserve the above-mentioned stability properties.

  • Keywords

Neutral delay differential equations, Pantograph delay, Asymptotic stability, Runge-Kutta methods, L-stable.

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COPYRIGHT: © Global Science Press

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@Article{JCM-22-523, author = {Jingjun and Zhao and and 15929 and and Jingjun Zhao and Wanrong and Cao and and 15931 and and Wanrong Cao and Mingzhu and Liu and and 15932 and and Mingzhu Liu}, title = {Asymptotic Stability of Runge-Kutta Methods for the Pantograph Equations}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {4}, pages = {523--534}, abstract = {

This paper considers the asymptotic stability analysis of both exact and numerical solutions of the following neutral delay differential equation with pantograph delay.

image.png

where $B,C,D\in C^{d\times d},q\in (0,1)$,and $B$ is regular. After transforming the above equation to non-automatic neutral equation with constant delay, we determine sufficient conditions for the asymptotic stability of the zero solution. Furthermore, we focus on the asymptotic stability behavior of Runge-Kutta method with variable stepsize. It is proved that a L-stable Runge-Kutta method can preserve the above-mentioned stability properties.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8861.html} }
TY - JOUR T1 - Asymptotic Stability of Runge-Kutta Methods for the Pantograph Equations AU - Zhao , Jingjun AU - Cao , Wanrong AU - Liu , Mingzhu JO - Journal of Computational Mathematics VL - 4 SP - 523 EP - 534 PY - 2004 DA - 2004/08 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8861.html KW - Neutral delay differential equations, Pantograph delay, Asymptotic stability, Runge-Kutta methods, L-stable. AB -

This paper considers the asymptotic stability analysis of both exact and numerical solutions of the following neutral delay differential equation with pantograph delay.

image.png

where $B,C,D\in C^{d\times d},q\in (0,1)$,and $B$ is regular. After transforming the above equation to non-automatic neutral equation with constant delay, we determine sufficient conditions for the asymptotic stability of the zero solution. Furthermore, we focus on the asymptotic stability behavior of Runge-Kutta method with variable stepsize. It is proved that a L-stable Runge-Kutta method can preserve the above-mentioned stability properties.

Jingjun Zhao, Wanrong Cao & Mingzhu Liu. (1970). Asymptotic Stability of Runge-Kutta Methods for the Pantograph Equations. Journal of Computational Mathematics. 22 (4). 523-534. doi:
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