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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Vydané v:Computers & mathematics with applications (1987) Ročník 62; číslo 4; s. 1619 - 1626
Hlavní autori: Chi, Guangsheng, Li, Gongsheng, Jia, Xianzheng
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Ltd 01.08.2011
Predmet:
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
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Shrnutí: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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content type line 23
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2011.02.029