多延迟微分方程θ-方法的GPL_m-稳定性  

GPL_m-stability of the θ-methods for differential equation with several delays

作　　者：徐阳[1] 赵景军[1] 刘明珠[1] 

机构地区：[1]哈尔滨工业大学理学院,黑龙江哈尔滨150001

出　　处：《黑龙江大学自然科学学报》2005年第6期707-709,715,共4页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(10271036)

摘　　要：研究多延迟微分方程θ-方法的稳定性.通过分析相应特征方程根的性质,给出系统稳定的一个充分条件.进一步,引入数值方法GPLm-稳定的定义,证明当且仅当θ=1时,线性θ-方法将保持系统解析解不依赖于延迟的稳定性质.The stability of θ- methods for the differential equation with several different delays is considered. By studying the properties of roots for the corresponding characteristic equation, the sufficient conditions under which the equation is stable are given. Furthermore, the definition of GPLm -stability for numerical methods is introduced. It is proved that the linear θ- method preserves the delay - independent stability of its exact solutions if and only if θ= 1.

关 键 词：延迟微分方程 稳定性 数值方法 

分 类 号：O241.8[理学—计算数学]