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

Abstract

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.

A fitted operator numerical method for singularly perturbed Fredholm integro-differential equation with integral initial condition

“…The method was 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. Amirali et al [ 1 ] proposed a fitted difference scheme for first-order singularly perturbed quasilinear Fredholm integro-differential equation with integral boundary conditions using exponential basis functions, quadrature interpolation rules and the method of integral identities.…”