Numerical computation for advection-diffusion model

Addiction-advection equation is a partial differential equation which has many applications in industry and searching for accurate numerical methods to solve it is of great importance. In this work, we propose two methods, the finite difference method (FDM) and the finite volume method (FVM). A discretization of the space fractional advection-diffusion model was used in both methods. The fractional derivatives terms are discretized using fractionally shifted Grünwald formulas. We compare the solutions of these two methods for a case study with an exact solution.