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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 740385, 14 pages
http://dx.doi.org/10.1155/2012/740385
Research Article

Numerical Identification of Multiparameters in the Space Fractional Advection Dispersion Equation by Final Observations

1Institute of Applied Mathematics, Shandong University of Technology, Zibo 255049, China
2Department of Basic Courses, Shandong Kaiwen College of Science and Technology, Jinan 250020, China

Received 6 September 2012; Accepted 13 November 2012

Academic Editor: Bo Han

Copyright © 2012 Dali Zhang et al. 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

This paper deals with an inverse problem for identifying multiparameters in 1D space fractional advection dispersion equation (FADE) on a finite domain with final observations. The parameters to be identified are the fractional order, the diffusion coefficient, and the average velocity in the FADE. The forward problem is solved by a finite difference scheme, and then an optimal perturbation regularization algorithm is introduced to determine the three parameters simultaneously. Numerical inversions are performed both with the accurate data and noisy data, and several factors having influences on realization of the algorithm are discussed. The inversion solutions are in good approximations to the exact solutions demonstrating the efficiency of the proposed algorithm.