Numerical simulation and parameters inversion for non-symmetric two-sided fractional advection-dispersion equations

This paper deals with numerical solution and parameters inversion for a one-dimensional non-symmetric two-sided fractional advection-dispersion equation (FADE) with zero Neumann boundary condition in a finite domain. A fully discretized finite difference scheme is set forth based on Grunwald-Letnikov's definition of the fractional derivative, and its stability and convergence are proved by estimating the spectral radius of the coefficient matrix of the scheme. Furthermore, an inverse problem of simultaneously determining the fractional order and the dispersion coefficients is investigated, and numerical inversions are carried out by using the optimal perturbation regularization algorithm. The inversion results show that the fractional order and the dispersion coefficients in the FADE can be determined successfully by the final observations.