标题：Numerical simulation and parameters inversion for non-symmetric two-sided fractional advection-dispersion equations
作者：Jia, Xianzheng; Li, Gongsheng
作者机构：[Jia, Xianzheng; Li, Gongsheng] Shandong Univ Technol, Inst Appl Math, 12 Zhangzhou Rd, Zibo 255049, Shandong, Peoples R China.
会议名称：3rd International Workshop on Computational Inverse Problems and Applications
会议日期：JUL 08-12, 2013
来源：JOURNAL OF INVERSE AND ILL-POSED PROBLEMS
关键词：Fractional advection-dispersion equation; Grunwald-Letnikov derivative;; finite difference scheme; stability and convergence; simultaneous; inversion; numerical simulation
摘要：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.