A NEW REGULARIZATION METHOD FOR THE TIME FRACTIONAL INVERSE ADVECTION-DISPERSION PROBLEM

In this paper, we consider the time fractional inverse advection-dispersion problem (TFIADP) in a quarter plane. The solute concentration and dispersion flux are sought from a measured concentration history at a fixed location inside the body. Such a problem is obtained from the classical advection-...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 2011-01, Vol.49 (5/6), p.1972-1990
Main Authors: ZHENG, G. H., WEI, T.
Format: Article
Language:English
Subjects:
A priori knowledge
Advection
Applied mathematics
Approximation
Control theory
Exact sciences and technology
Fourier transformations
Fourier transforms
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Perceptron convergence procedure
Random walk
Real functions
Regularization methods
Research universities
Sciences and techniques of general use
Sine function
Solutes
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Summary:In this paper, we consider the time fractional inverse advection-dispersion problem (TFIADP) in a quarter plane. The solute concentration and dispersion flux are sought from a measured concentration history at a fixed location inside the body. Such a problem is obtained from the classical advection-dispersion equation by replacing the first-order time derivative with the Caputo fractional derivative of order α (0 < α < 1). We show that the TFIADP is severely ill-posed, and we further apply a new regularization method to solve it based on the solution given by the Fourier method. Convergence estimates are presented under a priori bound assumptions for the exact solution. Finally, one numerical example is given to show that the proposed numerical method is effective.
ISSN:0036-1429
1095-7170
DOI:10.1137/100783042