摘要
数值求解延迟微分方程的Runge-kutta方法和θ-方法已经有了较深入的研究。本文适当改造求解常微分方程的Rosenbrock方法,构造了一类求解延迟微分方程的Rosenbrock方法,证明了这类方法是GP-稳定的,而且这类方法的GP-稳定性与求解常微分方程的Rosenbrock方法的A-稳定性等价。数值试验表明这类方法是有效的。
Runge-kutta methods andθ-methods in the numerical solution of delay differential equations have been deeply studied. In this paper we make proper modifications about a class of Rosenbrock methods for solving ordinary differential equations. A class of Rosenbrock methods for solving delay differential equations is constructed by Hout interpolation technics. It is proved that these methods are GP-stable. Moreover, GP-stability of this class of methods is equivalent to A-stability of Rosenbrock methods in the numerical solution of ordinary differential equations. Numerical experiment shows that the methods are efficient.
出处
《系统仿真学报》
CAS
CSCD
2002年第3期290-292,共3页
Journal of System Simulation
基金
湖南省教育厅资助科研项目
