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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.

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-22-523, author = {Zhao , JingjunCao , Wanrong and Liu , Mingzhu}, 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.

Zhao , JingjunCao , Wanrong and Liu , Mingzhu. (2004). Asymptotic Stability of Runge-Kutta Methods for the Pantograph Equations. Journal of Computational Mathematics. 22 (4). 523-534. doi:
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