In this paper, a system of singularly perturbed Volterra integro-differential equations is considered. The backward Euler formula is used to discretize the differential part and the right-hand rectangle rule is applied to approximate the integral term. The stabilities of the continuous and discrete solutions are carried out using the Grönwall’s inequality, respectively. The a posterior error bounds are given to design an adaptive grid generation algorithm. Numerical results complement the theoretical results.

中文翻译：

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奇摄动Volterra积分微分方程系统的最大范数后验误差估计

在本文中，考虑了一个奇摄动的Volterra积分微分方程组。后向欧拉公式用于离散化微分部分，右手矩形规则用于近似积分项。连续解和离散解的稳定性分别使用Grönwall不等式进行。给出了后验误差界限，以设计一种自适应网格生成算法。数值结果补充了理论结果。