多延迟向前型微分方程Runge-Kutta方法的数值稳定性

Stability of Runge-Kutta Methods in the Numerical Solution of Multi-delay Differential Equations of Advanced Type

本文讨论了应用Runge-Kutta方法于多延迟向前型分段连续型微分方程的数值稳定性,得到了数值解渐近稳定的条件,进一步地,利用Order-Star和Pade′逼近理论,给出了当数值方法的稳定函数是e^x的Pade′逼近时数值解的稳定区域包含解析解的稳定区域的充分必要条件,最后做了相关的数值实验验证了理论结果.

This paper is concerned with the stability analysis of the Runge–Kutta methods for the equation u′(t)=au(t)+a0u([t])+a1u([t+1])+a2u([t+2])+a3u([t+3]),The stability regions for the Runge–Kutta methods are determined.We make further use of the Order stars and(r,s)-Pade'approximation theorems,the conditions that the analytic stability region is contained in the numerical stability region are obtained when the stability function is given by the(r,s)-Pad e′approximation to the exponential e x.At last some numerical experiments are given.