多延迟微分代数方程θ-方法的渐近稳定性(英文)

Asymptotic stability of θ-methods for differential-algebraic equations with several delays

考虑线性多延迟微分代数方程θ-方法的渐近稳定性。通过分析相应的特征方程根的性质,给出多延迟微分代数方程解析解的渐近稳定的一个充分条件,进一步,应用特征方程根的性质,得出一个关于线性θ-方法与新θ-方法对方程解析解的渐近稳定性保持的充分条件:当θ∈(1/2,1]时,线性θ-方法与新θ-方法都是渐近稳定的。

Asymptotic stability of θ-methods for linear differential-algebraic equations with several delays is considered. By studying the roots of corresponding characteristic equation obtained by its exponential solution, a sufficient condition is given for asymptotic stability of linear differential-algebraic equations with several delays. Furthermore, through the analysis of characteristic roots, a sufficient condition is obtained for the linear θ-method and the new θ-method to preserve the corre-sponding asymptotic stability of the system, i.e., the linear θ-method and the new θ-method are asymptotically stable if θ∈(1/2, 1].