Numerical Methods for a Diffusive Class of Nonlocal Operators

In this paper we develop a numerical scheme based on quadratures to approximate solutions of integro-differential equations involving convolution kernels, $$\nu $$ , diffusive type. particular, assume is symmetric and exponentially decaying at infinity. We consider problems posed in bounded domains $${\mathbb {R}}$$ . the case with nonlocal Dirichlet boundary conditions, show convergence for kernels that have positive tails, but can take negative values. When are all our converges nonnegative kernels. Since Neumann conditions lead an equivalent formulation as unbounded case, these last results also apply problem.