In this article, we consider a class of singularly perturbed differential equations of convection‐diffusion type with nonlocal boundary conditions. A uniformly convergent numerical method is constructed via nonstandard finite difference and numerical integration methods to solve the problem. The nonlocal boundary condition is treated using numerical integration techniques. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be ϵ‐uniformly convergent.

中文翻译：

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非局部边界条件奇摄动对流扩散型问题的一致收敛数值方法

在本文中，我们考虑一类具有非局部边界条件的对流扩散型奇摄动微分方程。通过非标准有限差分和数值积分方法构造了一个统一收敛的数值方法来解决该问题。使用数值积分技术处理非局部边界条件。对于所考虑的数值示例，将不同的摄动参数值和网格大小的最大绝对误差和收敛速率列表化。该方法被示出为ε -uniformly收敛。