一类具有n阶转向点的大参数奇摄动方程的渐近解（英文）  

Asymptotic Solutions of Singularly Perturbed Equations for Large Parameter with Turning Point of n-th Order

作　　者：史娟荣[1,2] 

机构地区：[1]安徽机电职业技术学院基础教学部,芜湖241002 [2]上海交通大学数学系,上海200240

出　　处：《工程数学学报》2015年第6期920-926,共7页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(11202106);the Natural Science Foundation of the Education Deparment of Anhui Province(KJ2015A418)

摘　　要：本文研究了一类具有n阶转向点的大参数奇摄动方程解的渐近表达式.首先,利用Liouville-Green变换分别构造出当n为偶数和奇数情形下方程的外部解;随后,通过引入伸展变量,利用Bessel函数,我们分别构造出当n为偶数和奇数情形下方程在n阶转向点x=0附近的内层解;最后,我们利用匹配原理确定了外部解和内层解中的任意常数,从而得到方程的一致有效的一阶渐近表达式.This paper considers the asymptotic solutions of a class of singularly perturbed equations for larger parameter with turning point of n-th order. Firstly, the outer solution when n is odd or even, respectively, is obtained by using the Liouville- Green transformation. Then, the interior layer solution near the x = 0 when n is odd or even is constructed by introducing the stretching transformation and using the Bessel function. Finally, the arbitrary constants for the outer solution and interior layer solution are determined by using the matching principle. Thus, we obtain the uniformly valid asymptotic expression of the equation.

关 键 词：转向点 Liouville—Green变换 BESSEL函数 奇异摄动问题 

分 类 号：O175.14[理学—数学]