Asymptotic Stability of Runge-Kutta Methods for the Pantograph Equations

Asymptotic Stability of Runge-Kutta Methods for the Pantograph Equations

Year:    2004

Author:    Jingjun Zhao, Wanrong Cao, Mingzhu Liu

Journal of Computational Mathematics, Vol. 22 (2004), Iss. 4 : pp. 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.

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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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2004-JCM-8861

Journal of Computational Mathematics, Vol. 22 (2004), Iss. 4 : pp. 523–534

Published online:    2004-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

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

Author Details

Jingjun Zhao

Wanrong Cao

Mingzhu Liu