具有多外延时量微分方程Runge-Kutta方法的GP_mL-稳定性(英文)

The GP_mL-Stability of Runge-Kutta Methods for Differential System with many delays

研究Runge－Kutta方法的GPmL-稳定性，着重研究用隐式Runge－Kutta方法去解如下方程时的数值稳定性，y’=（t）=Ly（t）＋M1y（t-τ1）＋…＋Mmy（t-τm），t≥0，y（t）=Φ（t），t＜0，其中L，Mi（i=1，…，m）是N×N复矩阵，0＜τ1≤τ2≤…≤τm，Φ（t）是一个已知向量函数，证明隐式RK方法是GPmL-稳定的当且仅当它是L-稳定的．

This paper deals with the GPmL－stability of Runge－Kutta methods for the numerical solution of the system of differenml equations with many delays．We focus on the stability behaviour of Implicit Runge-Kutta methods（IRK）in the solutions of the following test System with m delay terms where L，Mi，（i=1，…，m） are complex matrices，and Φ（t） is a given vector function．We shall show that the IRK is GPm L－stable if and only if it is L－stable．