Solving singularly perturbed fredholm integro-differential equation using exact finite difference method.

Objectives: In this paper, a numerical scheme is designed for solving singularly perturbed Fredholm integro-differential equation. The scheme is constructed via the exact (non-standard) finite difference method to approximate the differential part and the composite Simpson's 1/3 rule for the integral part of the equation.

Result: The stability and uniform convergence analysis are demonstrated using solution bound and the truncation error bound. For three model examples, the maximum absolute error and the rate of convergence for different values of the perturbation parameter and mesh size are tabulated. The computational result shows, the proposed method is second-order uniformly convergent which is in a right agreement with the theoretical result.