一类前向时滞微分方程Runge-Kutta方法的振动性  

Oscillation of Runge-Kutta Methods for a Kind of Delay Differential Equations of Advanced Type

作　　者：银鹤凡 王琦[1] YIN Hefan;WANG Qi(School of Mathematics and Statistics,Guangdong University of Technology,Guangzhou 510006,China)

机构地区：[1]广东工业大学数学与统计学院,广东广州510006

出　　处：《湖南科技大学学报（自然科学版）》2023年第1期116-124,共9页Journal of Hunan University of Science And Technology：Natural Science Edition

基　　金：国家自然科学基金资助项目(11201084);广东省自然科学基金资助项目(2017A030313031)。

摘　　要：研究了一类特殊时滞微分方程——前向分段连续型微分方程数值解的振动性.利用Runge-Kutta方法对方程进行离散,得到数值方法保持解析解振动性的条件.同时讨论了稳定性与振动性的关系.最后给出几个数值例子来验证相应的结果.The paper focuses on the oscillation of numerical solution of a special kind of delay differential equations:differential equations with piecewise continuous arguments of advanced type.The Runge-Kutta methods are applied to discretize the mentioned equation,and the conditions of numerical methods preserve the oscillation of analytic solution are obtained.At the same time,this paper also discusses the relationship between stability and oscillation.Finally,several numerical examples are given to verify the corresponding results.

关 键 词：RUNGE-KUTTA方法 数值解 振动 非振动 

分 类 号：O241[理学—计算数学]