多延迟微分方程数值解θ－方法的稳定性

The Stability of the New θ-method in the Numerical Solution of Delay Differential Equations with Several Delay Terms

研究延迟微分方程（ＤＤＥ）数值解的稳定性。主要分析用新θ－方法解一般线性试验方程ｙ＇（ｔ）＝αｙ（ｔ）＋ｂ１ｙ（ｔ－τ１）＋ｂ２ｙ（ｔ－τ２）＋．．．＋ｙ（ｔ－τｓ），其中α∈Ｃ，ｂｊ∈Ｃ，τｊ＞０，ｊ＝１，２，．．．，Ｓ，所得到的数值解的性态。

This paper deals with the stability analysis of numerical method for delay differential equations(DDEs), and focuses on the stability behaviuour of the new θ-method in the solution of the general linear test equation.y'(t) = αy(t) + b1y(t- τ1) + b2y(t- τ2) + ... + bsy(t-τs)with τj>0, j= 1, 2, ... s and complex α, b1, b2, ..., bs. It is shown that the new θ-method is GPs-stable if and only if 1/2≤0≤1.