A novel numerical approach for Fredholm integro-differential equations

We examine the numerical solution of a second-order linear Fredholm integro-differential equation (FIDE) by a finite difference method. The discretization of the problem is obtained by a finite difference method on a uniform mesh. We construct the method using the integral identity method with basis functions and dealing with the integral terms by interpolating quadrature rules with remainder terms. We further employ the factorization method to establish the algorithm. We demonstrate the error estimates and the convergence of the method. The numerical results are enclosed to verify the order of accuracy.