多个滞时微分方程的Runge－Kutta法的数值稳定性分析  

Numerical Stability Analysis of Runge-Kutta Methods for Delay Differential Equations with Several Delay Terms

作　　者：田红炯 匡蛟勋 

出　　处：《上海师范大学学报（自然科学版）》1994年第2期95-101,共7页Journal of Shanghai Normal University(Natural Sciences)

摘　　要：本文将Ｒｕｎｇｅ－Ｋｕｔｔａ法应用于解多个滞时的微分方程．主要研究该方法数值解线性试验方程ｙ＇（ｔ）＝ａｙ（ｔ）十ｂ１ｙ（ｔ—τ１）十ｂ２ｙ（ｔ—τ２）（其中τ２≥，τ１＞０，ａ，ｂ１，ｂ２为复数）的稳定性态．我们证明满足条件ｄｅｔ（Ｉ—ｘＡ）＝０ｄｅｔ［Ｉ—Ａ十ｘｅｂＴ」≠０（ｘ∈Ｃ）的Ｒｕｎｇｅ－Ｋｕｔｔａ法是ＧＰ－稳定的当且仅当该方法是Ａ－稳定的．This paper deals with adapting Runge-Kutta methods to differential equations with several delay terms. We focus on the stability behaviour of the RungeKutta method in the soluting of the linear test equation y' (t) = ay (t) + b1y (t-τ1)+b2y(t-τ2), With τ2 ≥ τ1 > 0 and complex a,b1,b2. We prove that the Runge-Kutta method which satisfies det (I-xA ) = 0det[I -xA+xebT] ≠ 0 (whenever x ∈C) is GP2- stable if and only if the method is A -stable.

关 键 词：滞时微分方程 数值解 RUNGE-KUTTA法 插值过程 数值稳定性 P_2-稳定 GP_2-稳定 

分 类 号：O175.13[理学—数学]