延迟积分微分方程线性多步方法的稳定性分析  

Stability Analysis of Linear Multistep Methods for Delay Integro-Differential Equatioins

作　　者：刘建国[1] 姚金然[2] 卢菁菁[1] 

机构地区：[1]中南大学数学科学与计算技术学院,长沙410075 [2]黄山学院数学系,黄山245041

出　　处：《数学理论与应用》2008年第4期45-48,共4页Mathematical Theory and Applications

摘　　要：考虑带常延迟的延迟积分微分方程线性系统零解的渐近稳定性,本文采用拉格朗日插值的线性多步方法,探讨了系统数值方法的线性稳定性。证明了所有A-稳定且强零-稳定的Pouzet型线性多步方法能够保持原线性系统的延迟不依赖稳定性。For a linear system of delay integro- differential equations with a constant delay whose zero solution is asymptotically stable, this paper deals with the linear stability of numerical methods for the system. The adaptation of linear multistep methods with a Lagrange interpolation is considered. It is proven that every A-stable, strongly zero-stable linear muhistep methods of Pouzet type ean preserve the delay- independent stability of the underlying linear systems.

关 键 词：延迟积分微分方程 Pouzet型线性多步法 拉格朗日插值 渐近稳定性 

分 类 号：O175[理学—数学]