@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.

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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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8861.html} }