Using radial basis function-generated quadrature rules to solve nonlocal continuum models

The goal of this work is to expand on a previously devised approach for approximating nonlocal diffusion and nonlocal anomalous diffusion models with continuous solutions which used radial basis functions to generate accurate quadrature rules for the nonlocal integrals. We extend this approach to solve nonlocal models for convection-diffusion problems and nonlinear advection problems such as Burgers' equation. In addition, nonlocal problems with discontinuous solutions are considered for cases where the location of the discontinuity is known exactly and when the location is known to be in an interval dependent upon the grid spacing.