A Uniform Accurate Boundary Treatment for the One-Dimensional Non-Local Models

A uniform boundary treatment is proposed to construct the exact artificial boundary conditions for the one-dimensional non-local models. To this end, we first convert the governing equation of the non-local model into a semi-discretized version, and then an accurate numerical method is proposed for computing the Green’s function for the semi-discretized non-local model. These Green’s functions are then used to build the exact boundary conditions corresponding to the semi-discretized model. The numerical method is applied for three non-local models. The numerical results illustrate the efficiency of the boundary conditions.