Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 233, Issue 10, Pages 2631-2640Publisher
ELSEVIER
DOI: 10.1016/j.cam.2009.11.009
Keywords
Spectral regularization method; Cauchy problem; Time fractional advection-dispersion equation; Caputo fractional derivative; Fourier transform; Convergence estimate
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Funding
- NSF of China [10971089, 10671085]
- NCET of China
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In this paper, a Cauchy problem for the time fractional advection-dispersion equation (TFADE) is investigated. Such a problem is obtained from the classical advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order alpha (0 < alpha <= 1). We show that the Cauchy problem of TFADE is severely ill-posed and further apply a spectral regularization method to solve it based on the solution given by the Fourier method. The convergence estimate is obtained under a priori bound assumptions for the exact solution. Numerical examples are given to show the effectiveness of the proposed numerical method. (C) 2009 Elsevier B.V. All rights reserved.
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