(untitled) (Journal of Computational Mathematics, 2004)
This paper considers the asymptotic stability analysis of both exact and numerical solutions of the following neutral delay differential equation with pantograph delay. where B,C,DC^d× 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 L-stable Runge-Kutta method can preserve the above-mentioned stability properties.