关于非线性时滞微分系统的R-K方法的稳定性  

On the stability of R-K methods for non-linear variable delay systems

作　　者：梅家斌[1] 王洪山[1] 

机构地区：[1]武汉科技学院数理系,武汉430073

出　　处：《华中师范大学学报（自然科学版）》2003年第1期1-2,20,共3页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金资助项目(79870091).

摘　　要：具有时滞微分系统的稳定性问题是近年来讨论的热门话题.迄今,有关时滞微分系统稳定性的概念和结论都仅限于常时滞问题且都只考虑定步长的情况.本文在此基础上对变时滞变步长的情况进行了研究,并证明了在变时滞状态下,具有代数稳定的非线性微分系统的Runge-Kutta方法(简称R-K方法)仍然是零稳定的结论.The disscussion on delay differential system was widely concerned in recent years. Some concepts of stability of delay system as well as the relevant conclusions were limited actually in the part of to . All of these were under the conditions of constant delay and invariable stepsize. The paper turned to the study of variable delay and stepsize and proved that the RungeKutta method of nonlinear differential system of algebra stability was also of zerostabicity.

关 键 词：非线性时滞微分系统 R-K方法 代数稳定性 变步长 零稳定 

分 类 号：O175.14[理学—数学] O175.13[理学—基础数学]