Numerical inversions of a source term in the FADE with a Dirichlet boundary condition using final observations

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...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) Vol. 62; no. 4; pp. 1619 - 1626
Main Authors: Chi, Guangsheng, Li, Gongsheng, Jia, Xianzheng
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.08.2011
Subjects:
Algorithms
Boundary conditions
Dirichlet problem
Fractional advection–dispersion equation (FADE)
Inverse problems
Inversions
Mathematical analysis
Mathematical models
Numerical inversion
Optimal perturbation regularization algorithm
Perturbation methods
Source term inversion
Fractional advection–dispersion equation (FADE)
Source term inversion
Optimal perturbation regularization algorithm
Numerical inversion
ISSN:0898-1221, 1873-7668
Online Access:Get full text
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Summary: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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ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2011.02.029