This paper proposes a higher-order numerical approximation scheme to solve singularly perturbed reaction–diffusion boundary value problems. The proposed scheme is a combination of a fourth-order numerical difference method and classical central difference method applied on a non-equidistant grid. The non-equidistant grid is generated by equi-distributing a non-negative monitor function. The theoretical and empirical error analysis demonstrate that the proposed scheme has fourth-order uniform convergence with respect to the perturbation parameter.

中文翻译：

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奇异摄动反应扩散问题的高阶精确差分逼近使用网格等分布

本文提出了一种高阶数值近似方案来解决奇异摄动反应-扩散边界值问题。所提出的方案是应用在非等距网格上的四阶数值差分方法和经典中心差分方法的组合。非等距网格是通过等分布非负监控函数生成的。理论和经验误差分析表明，所提出的方案相对于扰动参数具有四阶一致收敛性。