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 Shishkin mesh. The method 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.
"Fitted second order numerical method for a singularly perturbed Fredholm integro-differential equation." Bull. Belg. Math. Soc. Simon Stevin 27 (1) 71 - 88, may 2020. https://doi.org/10.36045/bbms/1590199305