Numerical inversions of a source term in the FADE with a Dirichlet boundary condition using final observations |
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Authors: | Guangsheng Chi Gongsheng Li Xianzheng Jia |
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Affiliation: | a Institute of Applied Mathematics, Shandong University of Technology, Zibo, 255049, PR Chinab Shandong Kaiwen College of Science and Technology, Jinan, 250200, PR China |
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Abstract: | This paper deals with an inverse problem of determining a source term in the one-dimensional fractional advection-dispersion equation (FADE) with a Dirichlet boundary condition on a finite domain, using final observations. On the basis of the shifted Grünwald formula, a finite difference scheme for the forward problem of the FADE is given, by means of which the source magnitude depending upon the space variable is reconstructed numerically by applying an optimal perturbation regularization algorithm. Numerical inversions with noisy data are carried out for the unknowns taking three functional forms: polynomials, trigonometric functions and index functions. The reconstruction results show that the inversion algorithm is efficient for the inverse problem of determining source terms in a FADE, and the algorithm is also stable for additional data having random noises. |
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Keywords: | Fractional advection-dispersion equation (FADE) Source term inversion Optimal perturbation regularization algorithm Numerical inversion |
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