A Uniform Numerical Method for Solving Singularly Perturbed Fredholm Integro-Differential Problem

Abstract

In this paper, we deal with a class of boundary-value problems for the singularly perturbed Fredholm integro-differential equation. To solve the problem, we construct a new difference scheme by the method of integral identities using interpolating quadrature rules with remainder terms in integral form. We prove that the method is convergent in the discrete maximum norm, uniformly with respect to the perturbation parameter. We present numerical experiments which support the theoretical results.