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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 954983, 9 pages
http://dx.doi.org/10.1155/2013/954983
Research Article

A New Numerical Algorithm for Solving a Class of Fractional Advection-Dispersion Equation with Variable Coefficients Using Jacobi Polynomials

1Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef 62511, Egypt

Received 17 August 2013; Accepted 17 September 2013

Academic Editor: Dumitru Baleanu

Copyright © 2013 A. H. Bhrawy. 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 propose Jacobi-Gauss-Lobatto collocation approximation for the numerical solution of a class of fractional-in-space advection-dispersion equation with variable coefficients based on Caputo derivative. This approach has the advantage of transforming the problem into the solution of a system of ordinary differential equations in time this system is approximated through an implicit iterative method. In addition, some of the known spectral collocation approximations can be derived as special cases from our algorithm if we suitably choose the corresponding special cases of Jacobi parameters and . Finally, numerical results are provided to demonstrate the effectiveness of the proposed spectral algorithms.