高阶非线性奇摄动微分方程的三点边值问题  

Singular Perturbation of Three-pointed Value Problem of High-order Nonlinear Differential Equation

作　　者：丁海云[1] 倪明康[2,3] 

机构地区：[1]上海海事大学数学系,上海200135 [2]华东师范大学数学系,上海200062 [3]上海高校计算科学E-研究院上海交大研究所,上海200240

出　　处：《应用数学学报》2013年第2期315-323,共9页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11071075;11171113);中国科学院知识创新工程重大项目(30921064;90820307);上海市自然科学基金(10ZR1409200)资助项目

摘　　要：本文讨论了一类高阶非线性奇摄动微分方程的三点边值问题.根据小参数的不同次幂,分情况补充相应的边界条件.运用边界层函数法,构造了形式渐近解,并得到解的存在唯一性和渐近解的一致有效性.最后用数值计算结果印证了结论.A class of singular perturbation of three-pointed value problem of high-order nonlinear differential equation is examined in this paper.Relative boundary conditions are supplemented according to the different order power of small parameter. Using the method of boundary functions, the asymptotic solution of this problem is shown and proved to be uniformly effective.The existence and uniqueness of the solution for the system has also been derived.Numerical result is presented, which supports the theoretical result.

关 键 词：奇摄动 渐近级数 边界层函数法 微分流形 

分 类 号：O175.14[理学—数学]