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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 303857, 9 pages
http://dx.doi.org/10.1155/2015/303857
Research Article

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

Department of Applied Mathematics, CIMAT, Jalisco s/n, 36240 Guanajuato, GTO, Mexico

Received 16 November 2014; Revised 15 January 2015; Accepted 17 January 2015

Academic Editor: Manuel De la Sen

Copyright © 2015 Silvia Jerez and Ivan Dzib. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.