一类特殊延迟微分方程的数值振动性  

Numerical Oscillation for a Special Kind of Delay Differential Equations

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

机构地区：[1]广东工业大学应用数学学院,广东广州510006

出　　处：《聊城大学学报（自然科学版）》2021年第2期1-7,共7页Journal of Liaocheng University:Natural Science Edition

基　　金：国家自然科学基金项目(61803095);广东省自然科学基金项目(2017A030313031,18ZK0174)资助。

摘　　要：针对一类特殊的延迟微分方程-超前型分段连续微分方程,讨论了数值解的振动性。用θ-方法对方程进行离散,获得了数值方法保持方程解析解振动性的条件。同时,分别针对解析解和数值解,深入讨论了动力学行为的四种不同状态。一些数值例子进一步验证了相应的结论。This paper is concerned with the oscillation of numerical solution of a special kind of delay differential equations:differential equations with piecewise continuous arguments of advanced type.Theθ-methods are extended to solve the mentioned equation,and the conditions for numerical methods inherit the oscillation of analytic solution are obtained.At the same time,four different states of dynamic behavior are discussed in detail for analytic solution and numerical solution,respectively.The presented numerical examples further testify the corresponding results.

关 键 词：Θ-方法 数值解 振动性 非振动性 

分 类 号：O241[理学—计算数学]