In this paper, a singularly perturbed Volterra integro- differential equation is being surveyed. On a piecewise-uniform Shishkin mesh, a fitted mesh finite difference approach is applied using a composite trapezoidal rule in the case of integral component and a finite difference operator for the derivative component. The proposed technique acquires a uniform convergence in accordance with the perturbation parameter. To improve the accuracy of the computed solution, an extrapolation, specifically Richardson extrapolation, is used measured in the discrete maximum norm and almost second-order convergence is attained. Further numerical results are provided to assist the theoretical estimates.

在本文中，正在调查一个奇异摄动的 Volterra 积分微分方程。在分段均匀 Shishkin 网格上，在积分分量和微分分量的有限差分算子的情况下，使用复合梯形规则应用拟合网格有限差分方法。所提出的技术根据扰动参数获得均匀收敛。为了提高计算解决方案的准确性，在离散最大范数中使用外推法，特别是理查森外推法，并获得几乎二阶收敛。提供了进一步的数值结果以帮助理论估计。