A Second-Order Post-processing Technique for Singularly Perturbed Volterra Integro-differential Equations

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.