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

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  • Zheng, G.H.
  • Wei, T.

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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  • Zheng, G.H. & Wei, T., 2010. "Spectral regularization method for the time fractional inverse advection–dispersion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(1), pages 37-51.
    • Handle: RePEc:eee:matcom:v:81:y:2010:i:1:p:37-51
    DOI: 10.1016/j.matcom.2010.06.017
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    1. Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
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    Cited by:

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    2. Marasi, H.R. & Derakhshan, M.H., 2023. "Numerical simulation of time variable fractional order mobile–immobile advection–dispersion model based on an efficient hybrid numerical method with stability and convergence analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 368-389.
    3. Yang, Fan & Fu, Chu-Li & Li, Xiao-Xiao, 2018. "The method of simplified Tikhonov regularization for a time-fractional inverse diffusion problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 144(C), pages 219-234.

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