Spectral regularization method for the time fractional inverse advection-dispersion equation
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 problem is obtained from the classical advection dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order alpha(0 < alpha < 1). We show that the TFIADP is severely ill-posed and further apply a spectral 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, numerical examples are given to show that the proposed numerical method is effective. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.
spectral regularization method time fractional inverse advection-dispersion equation caputo fractional derivatives convergence estimate fourier transform