A Discrete Method Based on the CE-SE Formulation for the Fractional Advection-Dispersion Equation - Silvia Jerez; Ivan Dzib (Discrete Dynamics in Nature and Society)
We obtain a numerical algorithm by using the space-time conservation element and solution element (CE-SE) method for the fractional advection-dispersion equation. The fractional derivative is defined by the Riemann-Liouville formula. We prove that the CE-SE approximation is conditionally stable under mild requirements. A numerical simulation is performed for the one-dimensional case by considering a benchmark with a discontinuous initial condition in order to compare the results with the analytical solution.