A Fitted Operator Finite Difference Approximation for Singularly Perturbed Volterra–Fredholm Integro-Differential Equations

Abstract

This paper presents a ε-uniform and reliable numerical scheme to solve second-order singularly perturbed Volterra–Fredholm integro-differential equations. Some properties of the analytical solution are given, and the finite difference scheme is established on a non-uniform mesh by using interpolating quadrature rules and the linear basis functions. An error analysis is successfully carried out on the Boglaev–Bakhvalov-type mesh. Some numerical experiments are included to authenticate the theoretical findings. In this regard, the main advantage of the suggested method is to yield stable results on layer-adapted meshes.