Abstract

MEJIA, Carlos  and  PIEDRAHITA H, Alejandro. Solution of a time fractional inverse advection-dispersion problem by discrete mollification. Rev.colomb.mat. [online]. 2017, vol.51, n.1, pp.83-102. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v51n1.66839.

We consider an inverse problem for a time fractional advection-dispersion equation in a 1-D semi-infinite setting. The fractional derivative is interpreted in the sense of Caputo and advection and dispersion coefficients are constant. The inverse problem consists on the recovery of the boundary distribution of solute concentration and dispersion flux from measured (noisy) data known at an interior location. This inverse problem is ill-posed and thus the numerical solution must include some regularization technique. Our approach is a finite difference space marching scheme enhanced by adaptive discrete mollification. Error estimates and illustrative numerical examples are provided.

Keywords : Ill-posed problems; Caputo fractional derivative; time fractional inverse advection-dispersion problem; finite differences; mollification.

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