Numerical Method Based on Galerkin Approximation for the Fractional Advection-Dispersion Equation

In this paper, we present a numerical method for solving homogeneous as well as non-homogeneous fractional advection-dispersion equation (FADE). The numerical method is based on the Galerkin approximation. The Galerkin approximation converts the FADE into a system of fractional ordinary differential equations whose solutions is discussed. Convergence of the proposed method is shown. Numerical examples are given and numerical results are compared with exact solution to show the effectiveness and accuracy of the proposed method.