中立型多延时微分代数系统线性多步法的渐近稳定性(英文)

Asymptotic Stability of Linear Multistep Methods for Neutral Differential-Algebraic Equations with Many Delays

文章讨论了用线性多步法求解线性中立型多延时微分代数系统的渐近稳定性.通过分析相应的特征方程根的性质,得出一个线性多步法渐近稳定的充分条件:线性多步法是A稳定的,并且它的第二特征多项式的根的模不等于1.

This paper discussed the asymptotic stability of linear multistep methods for the numerical solution of linear constant coefficient neutral differential - algebraic equations with many delays. By studying the roots of corresponding characteristic equation, we obtained that the linear muhistep method is asymptotically stable if it is A-stable and its second characteristic polynomial has no root z with ｜z｜ = 1.