非线性延迟积分微分方程线性多步法的渐近稳定性  

ASYMPTOTIC STABILITY OF LINEAR MULTISTEP METHODS FOR DELAY INTEGRO-DIFFERENTIAL EQUATIONS

作　　者：胡鹏[1] 黄乘明[1] 

机构地区：[1]华中科技大学数学与统计学院,湖北武汉430074

出　　处：《数值计算与计算机应用》2010年第2期116-122,共7页Journal on Numerical Methods and Computer Applications

基　　金：中国国家自然科学基金(No.10971077)

摘　　要：本文研究了非线性延迟积分微分方程线性多步法的渐近稳定性.证明了在约束网格下,带有复合求积公式A-稳定的线性多步法能够保持解析解的渐近稳定性.文章最后,数值试验验证了本文的结论.This paper deals with the asymptotic stability of linear multistep methods for nonlinear delay integro-differential equations. It is shown that, under constrained meshes, A-stable linear multistep methods with composite quadrature rules can preserve the asymptotic stability of the analytical solution. At last, we validate our conclusions by numerical experiments.

关 键 词：非线性延迟积分微分方程 A-稳定 线性多步法 渐近稳定性 

分 类 号：O175.6[理学—数学]