2020/03/30 by Libo Feng, Pinghui Zhuang, Feng, Libo +7
Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2003.13923
openalex publication_date 2020/03/30 · openalex created_date 2020/04/10 · openalex updated_date 2026/07/28
In this paper, we propose high-order numerical methods for the Riesz space\nfractional advection-dispersion equations (RSFADE) on a finite domain. The\nRSFADE is obtained from the standard advection-dispersion equation by replacing\nthe first-order and second-order space derivative with the Riesz fractional\nderivatives of order \α\∈(0,1) and \β\∈(1,2], respectively.\nFirstly, we utilize the weighted and shifted Gr "unwald difference operators to\napproximate the Riesz fractional derivative and present the finite difference\nmethod for the RSFADE. Specifically, we discuss the Crank-Nicolson scheme and\nsolve it in matrix form. Secondly, we prove that the scheme is unconditionally\nstable and convergent with the accuracy of mathcal O(\τ2+h2). Thirdly,\nwe use the Richardson extrapolation method (REM) to improve the convergence\norder which can be mathcal O(\τ4+h4). Finally, some numerical examples\nare given to show the effectiveness of the numerical method, and the results\nare excellent with the theoretical analysis.\n