High-order numerical methods for the Riesz space fractional advection-dispersion equations
| Autor: | Feng, Libo, Zhuang, Pinghui, Liu, Fawang, Turner, Ian, Li, Jing |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we propose high-order numerical methods for the Riesz space fractional advection-dispersion equations (RSFADE) on a {f}inite domain. The RSFADE is obtained from the standard advection-dispersion equation by replacing the first-order and second-order space derivative with the Riesz fractional derivatives of order $\alpha\in(0,1)$ and $\beta\in(1,2]$, respectively. Firstly, we utilize the weighted and shifted Gr\"unwald difference operators to approximate the Riesz fractional derivative and present the {f}inite difference method for the RSFADE. Specifically, we discuss the Crank-Nicolson scheme and solve it in matrix form. Secondly, we prove that the scheme is unconditionally stable and convergent with the accuracy of $\mathcal {O}(\tau^2+h^2)$. Thirdly, we use the Richardson extrapolation method (REM) to improve the convergence order which can be $\mathcal {O}(\tau^4+h^4)$. Finally, some numerical examples are given to show the effectiveness of the numerical method, and the results are excellent with the theoretical analysis. Comment: 14 pages, 4 figures. This article has been withdrawn from Computers and Mathematics with Applications due to the reason of the guest editor |
| Databáze: | arXiv |
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