A Fitted Operator Numerical Method for Singularly Perturbed Fredholm Integro-differential Equation with Non-local Initial Condition

Abstract

In this work, we construct a fitted finite difference scheme for singularly perturbed Fredholm integro-differential equation with non-local initial condition. To discretize the problem, a parameter-uniform numerical scheme was constructed, via fitted operator finite difference method to approximate the differential part and Simpson’s composite 1 3 rule for the inte gral part with an initial condition that also yields the remaining terms. Stability bound and the error estimation of the approximate solution are performed to show parameter-uniform convergence of the proposed scheme. We also demonstrate that the scheme is uniformly con vergent with order one. Numerical results are also provided for a couple of examples to support theoretical analysis.