线性多步法求解广义中立型滞时微分代数方程组的渐近稳定性(英文)

Asymptotic Stability of Linear Multistep Methods for Generalized Neutral Delay Differential-Algebraic Equations

讨论了广义中立型滞时微分代数方程组理论和数值解的渐近稳定性。得出一个广义中立型滞时微分代数方程组渐近稳定的充分条件。通过对相应特征方程的根的研究,证明了线性多步法渐近稳定的充分条件是:该线性多步法是A-稳定的,并且它的第二特征多项式的根的模不等于1。

The asymptotic stability of analytical and numerical solutions of generalized neutral delay differential-algebraic equations was discussed. A Sufficient condition was derived under which generalized neutral delay differential-algebraic equations are asymptotically stable. By studying the roots of the corresponding characteristic equation, it is shown that the linear multistep method is asymptotically stable if the linear multistep method is A-stable and its second characteristic polynomial has no root z with ｜z｜ = 1.