ASYMPTOTIC STABILITY OF RUNGE-KUTTA METHODS FOR THE PANTOGRAPH EQUATIONS

• 来源期刊: 计算数学(英文版)
• 关键词: Neutral delay differential equations Pantograph delay Asymptotic stability Runge-Kutta methods L-stable.
• 年，卷（期）: 2004,（4）
• 页码范围: 523-534
• 页数: 12页
• 语种: 英文

摘要

This paper considers the asymptotic stability analysis of both exact and numericalsolutions of the following neutral delay differential equation with pantograph delay.{x′(t)+Bx(t)+Cx′(qt)+Dx(qt)=0, t>0,x(0)=x0,where B, C, D ∈ Cd×d, q ∈ (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 Lstable Runge-Kutta method can preserve the above-mentioned stability properties.