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本文给出了延迟微分方程数值解的稳定性分析。重点解决了单腿θ—方法和线性θ—方法用于求解线性检验方程U(t)=λ(t)U(t)+μ(t)U(t-τ),其中τ>0,λ、μ是从实数域到复数域上的函数,证明了当0<θ<1时两种方法都是不稳定的;而当θ=1时是稳定的。
In this paper, the stability analysis of numerical solution of delay differential equations is given. The single leg θ-method and the linear θ-method are mainly used to solve the linear test equation U (t) = λ (t) U (t) + μ (t) U , Μ is a function from the real number field to the complex number field and it is proved that both methods are unstable when 0 <θ <1 and stable when θ = 1.