一类非线性时滞微分方程的奇异摄动研究  

Singularly Perturbed Study on a Class of Nonlinear Delay Differential Equation

作　　者：谢英超 程燕[2] 

机构地区：[1]陆军军官学院研究生管理大队,安徽合肥230031 [2]陆军军官学院基础部,安徽合肥230031

出　　处：《安徽师范大学学报（自然科学版）》2015年第2期129-133,共5页Journal of Anhui Normal University(Natural Science)

基　　金：国家自然科学基金项目(11202106);安徽省自然科学基金项目(1408085MA06)

摘　　要：研究了一类依赖于小参数的小时滞微分方程.首先利用拟合函数法将双参数问题转换为便于分析的单参数问题,再利用校正函数法得到了方程的一致有效的渐近解,并利用微分不等式理论给出了证明,最后将其与数值解进行了精度比较.结果表明该摄动方法是有效的,从而可以更好地分析这类方程的解的性态.In this paper,a class of small delay differential equation depending on a small parameter is considered.Firstly using the fitting function method,the two parameters problem is converted to a single parameter problem for facilitating analysis.Then using the correction function method,the uniformly valid asymptotic solution of the equation is obtained,which is proved by using the theory of differential inequalities.Finally it＇s compared with the numerical solution.The result shows that the perturbation method is effective,so we can analyze the behavior of solution for the class of delay differential equation much better.

关 键 词：奇异摄动 时滞微分方程 非线性 渐近解 

分 类 号：O175.7[理学—数学]