双小参数问题新颖的计算方法

A Novel Computational Method for Problem with Two Small Parameter

讨论双小参数奇摄动问题两点边值方程,提出新颖的计算方法,即将渐近解法和数值解法相结合.按渐近解法的思想将解析解分解为一个光滑部分和左右两个奇性部分,对这三部分都进行上界估计.光滑部分是二阶渐近逼近,可直接求解;对左右两个奇性部分分别构造Shishkin差分格式,新方法很好地拟合了两边边界层的性质.文后列举数值例子以说明理论分析的正确性.

Singularly perturbed two small parameter ODE with boundary value problem is considered. The novel numerical method, which is combining techmiques of asymptotic method and numerical method, is constructed. According to asympotic idea, the solution is decomposed into the smooth component and two singular component, one on the left side while the other on the right side. The upper bounds of the smooth corn-ponent and the singular components are studied. The smooth component, which is the two-order asympotic solution, can be solved easily. For the two singular components, the traditional Shishkin＇s scheme is con-structed respectively. The new method captures the property of boundary layer very well. Numerical result is given, which is in agreement with the theoretical results.