In this article, a boundary value problem for a nonlinear system of singularly perturbed two second order differential equations in which only the first equation is multiplied by a small positive parameter is considered. The first component of the solution exhibits boundary layers whereas the second component exhibits less-severe layers. A numerical method composed of a classical finite difference scheme applied on a piecewise uniform Shishkin mesh is suggested to solve the system. The method is proved to be essentially second order convergent in the maximum norm uniformly with respect to the perturbation parameter. Numerical illustration presented supports the proved theoretical results.

在本文中，考虑了奇异摄动的两个二阶微分方程的非线性系统的边值问题，其中只有第一方程乘以一个小的正参数。解决方案的第一部分表现出边界层，而第二部分表现出较不严重的层。提出了一种由应用于分段均匀 Shishkin 网格的经典有限差分格式组成的数值方法来求解该系统。证明该方法对于扰动参数在最大范数上基本上是二阶收敛的。给出的数值说明支持了已证明的理论结果。