Numerical inversions of a source term in the FADE with a Dirichlet boundary condition using final observations. (English) Zbl 1231.65158

Summary: We deal 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.


65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
35K20 Initial-boundary value problems for second-order parabolic equations
45K05 Integro-partial differential equations
Full Text: DOI


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