中立型延迟微分方程一般线性方法的非线性稳定性  

Nonlinear Stability of General Linear Methods for Neutral Delay Differential Equations

作　　者：李超群[1] 

机构地区：[1]中国地质大学数学系,武汉430074

出　　处：《应用数学学报》2008年第2期249-256,共8页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(No:10101027)资助项目.

摘　　要：本文研究一类非线性中立型延迟微分方程一般线性方法的数值稳定性.证明了一般线性方法为(k,p,0)一代数稳定时,在一定的约束条件下,其数值解保持微分方程理论解的稳定性质。This paper investigates the stability of the numerical solutions of general linear methods for a class of nonlinear neutral delay differential equations. It is shown that （k,p,0）-algebraically stable general linear methods, under some restrictions, preserves the analogous stability of the original differential equations. In particular, it is proven that all algebraically stable general linear methods with restricted mesh can preserve the stability of the underlying systems without conditions.

关 键 词：中立型延迟微分方程 一般线性方法 (k p 0)-代数稳定 代数稳定 

分 类 号：O241.8[理学—计算数学]