含变系数的二阶奇摄动问题的多层现象  

The Multi-layer Phenomenon on the Second Order Singularly Perturbation Problem with a Variable Coefficient

作　　者：胡永生[1] 

机构地区：[1]福建农业职业技术学院公共教学部,福建福州350007

出　　处：《闽南师范大学学报（自然科学版）》2017年第3期10-18,共9页Journal of Minnan Normal University：Natural Science

摘　　要：研究一类含有变系数的二阶奇摄动问题的多层现象.首先区分变系数的不同符号,把奇摄动问题划分为左(右)问题,由渐近展开法,分别构造了左(右)问题的外部解;通过引入伸长变量,各求得两个特异极限,进而获得左(右)问题的右(左)层函数和各自的中间层函数.再通过Van Dyke匹配原则对内外解进行匹配和"缝接",得到奇摄动问题的一致有效的渐近展开式,并通过一个数值算例来验证其有效性.This thesis aims at studying one kind of multi-layer phenomenon on the second order singular perturbation problem with a variable coefficient. Firstly, it distinguishes the different signs of the variable coefficient, and divides the singular perturbation problem into the left and the right problems to construct the outer solutions according to the asymptotic expansions method. Secondly, it makes use of the stretched variable to get the two distinguished limits and then to obtain the right-layer function of the left problem, the left-layer function of the right problem and the separate intermediate functions.Finally, the internal and the external solution are matched and spliced based on Van Dyke Matching Principle to reach the efficient asymptotic expansion of the singular perturbation problem, and the efficient asymptotic expansion is verified by an numerical example lastly.

关 键 词：变系数 特异极限 多层现象 VAN Dyke匹配原则 二阶奇摄动 

分 类 号：O175.8[理学—数学]