The aim of this paper is to present a monotone numerical method on uniform mesh for solving singularly perturbed three-point reaction–diffusion boundary value problems. Firstly, properties of the exact solution are analyzed. Difference schemes are established by the method of the integral identities with the appropriate quadrature rules with remainder terms in integral form. It is then proved that the method is second-order uniformly convergent with respect to singular perturbation parameter, in discrete maximum norm. Finally, one numerical example is presented to demonstrate the efficiency of the proposed method.

中文翻译：

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具有非局部边界条件的奇摄动问题的二阶数值方法

本文的目的是提出一种用于解决奇异摄动三点反应扩散边界值问题的均匀网格上的单调数值方法。首先，分析精确解的性质。通过具有适当的正交规则的积分身份的方法建立差分方案，其余项为积分形式。然后证明了该方法在离散最大范数下相对于奇异摄动参数是二阶均匀收敛的。最后，通过一个数值例子说明了该方法的有效性。