Amiraliyev, Gabil M.; Durmaz, Muhammet Enes; Kudu, Mustafa

In this paper, we consider the linear first order singularly perturbed Fredholm integro-differential equation. For the solution of this problem, fitted difference scheme is constructed on a Shishkinmesh. Themethod is based on the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder terms in integral form. The method is proved to be second-order convergent in the discrete maximum norm. Also, numerical results are given to support theoretical analysis.