Spectral regularization method for the time fractional inverse advection–dispersion equation

G.H. Zheng and T. Wei

Mathematics and Computers in Simulation (MATCOM), 2010, vol. 81, issue 1, 37-51

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.

Keywords: Spectral regularization method; Time fractional inverse advection–dispersion equation; Caputo fractional derivatives; Fourier transform; Convergence estimate (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:81:y:2010:i:1:p:37-51

DOI: 10.1016/j.matcom.2010.06.017

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