A stable numerical method for singularly perturbed Fredholm integro differential equation using exponentially fitted difference method

Abstract

This paper implemented a stable numerical scheme for solving singularly perturbed linear second-order Fredholm integro-differential equation. A parameter-uniform numerical method was constructed using an exponentially fitted finite difference method to approximate the differential part and the composite Simpson 1/3 rule for the integral part of the equation. The scheme’s stability and convergence analysis has been carried out. The maximum absolute errors and the rate of convergence are tabulated for different values of the perturbation parameter ɛ and mesh sizes using different numerical test examples.