First-order numerical method for the singularly perturbed nonlinear Fredholm integro-differential equation with integral boundary condition

In this work, we consider first-order singularly perturbed quasilinear Fredholm integro-differential equation with integral boundary condition. Building a numerical strategy with uniform ϵ-parameter convergence is our goal. With the use of exponential basis functions, quadrature interpolation rules and the method of integral identities, a fitted difference scheme is constructed and examined. The weight and remainder term are both expressed in integral form. It is shown that the method exhibits uniform first-order convergence of the perturbation parameter. Error estimates for the approximation solution are established and a numerical example is given to validate the theoretical findings.