Spectral regularization method for the time fractional inverse advection-dispersion equation |
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Authors: | G.H. Zheng |
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Affiliation: | School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, PR China |
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Abstract: | In this paper, we consider the time fractional inverse advection-dispersion problem (TFIADP) in a quarter plane. The solute concentration and dispersion flux are sought from a measured concentration history at a fixed location inside the body. Such problem is obtained from the classical advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α(0 < α < 1). We show that the TFIADP is severely ill-posed and further apply a spectral regularization method to solve it based on the solution given by the Fourier method. Convergence estimates are presented under a priori bound assumptions for the exact solution. Finally, numerical examples are given to show that the proposed numerical method is effective. |
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Keywords: | Spectral regularization method Time fractional inverse advection-dispersion equation Caputo fractional derivatives Fourier transform Convergence estimate |
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