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 - <p style="text-align: justify;">This paper considers the asymptotic stability analysis of both exact and numerical solutions of the following neutral delay differential equation with pantograph delay.<br/></p><p style="text-align:center"><img src="https://admin.global-sci.org/uploads/ueditor/image/20210519/1621419035711473.png" title="1621419035711473.png" alt="image.png" width="405" height="67"/></p><p style="text-align: justify;">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. <br/></p>