摘要
讨论了一类具有转向点的非线性奇摄动问题,首先用渐近展开法构造出该问题的外部解,通过引入伸长变量,得到在x=x0附近三种不同情形的内层解;利用Prandtl匹配原理,找到转向点的准确位置,并求出该问题的一阶一致有效的渐近展开式。最后将求得结果与数值解进行比较,得到较高的精度。
In this work a kind of non-linear singularly perturbed boundary value problems with turning points is studied. The method of matched asymptotic expansions is first used to construct the outer layer solu- tions, and by introducing the stretched variable, three kinds of interior layer solutions at x=x0 are obtained. Prandtl matching principle is used to get the positions of the turning points and to determine the first-order uniform asymptotic expansions. The obtained results show a high degree of accuracy by comparing with the numerical solution.
出处
《宿州学院学报》
2015年第4期89-91,共3页
Journal of Suzhou University
关键词
奇摄动
转向点
非线性
Prandtl匹配原理
singular perturbation
turning points
non-linear
prandtl matching principle
