【摘 要】
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This paper considers the asymptotic stability analysis of both exact and numericalsolutions of the following neutral delay differential equation with pantograph
【机 构】
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Department of mathematics, Harbin Institute of Technology, Harbin 150001, China
论文部分内容阅读
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.
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