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

Abstract

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.

A fitted operator numerical method for singularly perturbed Fredholm integro-differential equation with integral initial condition

“…They used a non-uniform mesh by using interpolating quadrature rules and the linear basis functions. Solomon et al [ 4 ] applied the exact difference method for solving reaction-diffusion type SPFIDE and established the uniform convergence analysis of the scheme.…”