In this paper, we propose and analyze numerical treatment for a singularly perturbed convection–diffusion boundary value problem with nonlocal condition. First, the boundary layer behavior of the exact solution and its first derivative have been estimated. Then we construct a finite difference scheme on a uniform mesh. We prove the uniform convergence of the proposed difference scheme and give an error estimate. We also present numerical examples, which demonstrate computational efficiency of the proposed method.

中文翻译：

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求解奇异摄动三点边值问题的差分格式

在本文中，我们提出并分析了具有非局部条件的奇异扰动对流-扩散边界值问题的数值处理方法。首先，已经估计了精确解的边界层行为及其一阶导数。然后我们在均匀网格上构造一个有限差分格式。我们证明了所提出的差分方案的一致收敛性并给出了误差估计。我们还提供了数值例子，证明了所提出方法的计算效率。