ASYMPTOTIC STABILITY OF RUNGE-KUTTA METHODS FOR THE PANTOGRAPH EQUATIONS  

作　　者：Jing-junZhao Wan-rongCao Ming-zhuLiu 

机构地区：[1]Departmentofmathematics,HarbinInstituteofTechnology,Harbin150001,China)

出　　处：《Journal of Computational Mathematics》2004年第4期523-534,共12页计算数学（英文）

摘　　要：This paper considers the asymptotic stability analysis of both exact and numerical solutions of the following neutral delay differential equation with pantograph delay.{x′(t)+Bxd(t)+Cx′(qt)+Dx(qt)=0,t>0,x(0)=X0,}where B, C, D∈C^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 Lstable Runge-Kutta method can preserve the above-mentioned stability properties.

分 类 号：O175.11[理学—数学]