A discretization method for nonlocal diffusion type equations

In this paper we consider a numerical scheme for the treatment of an integro-differential equation. The latter represents the formulation of a nonlocal diffusion type equation. The discretization procedure relies on the application of the line method. However, quadrature formulae are needed for the evaluation of the integral operator. They are based on generalized Bernstein polynomials. Numerical evidence shows that the proposed method is a suitable and reliable approach for the problem