Radau IIA方法对比例延迟微分方程的渐近稳定性  

Asymptotic Stability Properties of Radau IIA Methods for the Pantograph Delay Equation

作　　者：李冬松[1] 刘明珠[1] 

机构地区：[1]哈尔滨工业大学数学系,黑龙江省哈尔滨市150001

出　　处：《系统仿真学报》2002年第6期704-706,共3页Journal of System Simulation

基　　金：国家自然科学(No. 19871019)

摘　　要：研究Raudau IIA 方法用于求解比例延迟微分方程时的渐近稳定性。近年来比例延迟微分方程数值解的性质已被数位数学家所研究,他们使用的步长都是定步长,一般情况下将推导出较难分析的递推关系,在本文中出于理论和计算两方面的原因,我们研究强制变步长计算方案,这种解法得到不变阶差分方程。我们证明了Raudau IIA 方法是渐近稳定的。This paper deals with the asymptotic stability analysis of Radau IIA methods for the pantograph delay equation. In recent years stability properties of numerical methods for this kind of equation have been studied by numerous authors who have considered meshes with fixed mesh. In general the developed techniques give rise to a non-ordinary recurrence relation. In this paper we study constrained variable stepsize schemes, suggested by theoretical and computational reasons, which lead to a non- stationary difference equation. We prove that Radau IIA methods are H-stable.

关 键 词：RadauIIa方法 比例延迟微分方程 渐近稳定性 数值解 

分 类 号：O241.8[理学—计算数学]