A Discrete Method Based on the CE-SE Formulation for the Fractional Advection-Dispersion Equation

Abstract EN

We obtain a numerical algorithm by using the space-time conservation element and solution element (CE-SE) method forthe fractional advection-dispersion equation.

The fractional derivative is defined by the Riemann-Liouvilleformula.

We prove that the CE-SE approximation is conditionally stable undermild requirements.

A numerical simulation isperformed for the one-dimensional case by considering a benchmark with a discontinuous initial conditionin order to compare the results with the analytical solution.