分段连续型混合泛函多延迟微分方程Runge-Kutta方法的数值稳定性  

Numerical Stability of Runge-Kutta Methods of the Functional Multi-delay Differential Equations with Piecewise Continuous Arguments

作　　者：王琦[1] 

机构地区：[1]广东工业大学应用数学学院,广州510006

出　　处：《西南大学学报（自然科学版）》2011年第7期16-20,共5页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(51008084);广东省自然科学基金资助项目(9451009001002753)

摘　　要：将Runge-Kutta方法用于求解自变量分段连续型混合泛函多延迟微分方程,得到了数值解渐近稳定的条件.利用Padé逼近理论得到了数值解的渐近稳定区域包含解析解的渐近稳定区域的充分必要条件,并给出了几个数值算例.By application of Runge-Kutta methods to solving the functional multi-delay differential equations with piecewise continuous arguments,the conditions under which the numerical solution is asymptotically stable are obtained.By means of the theory of Padé approximation,the necessary and sufficient conditions under which the numerical stability region contains the analytic stability region are obtained and some numerical experiments are given.

关 键 词：分段连续 延迟微分方程 渐近稳定性 RUNGE-KUTTA方法 

分 类 号：O241.81[理学—计算数学]