论文标题
Riesz空间分数对流分散方程的高阶数值方法
High-order numerical methods for the Riesz space fractional advection-dispersion equations
论文作者
论文摘要
在本文中，我们建议在{f} inte域上的Riesz空间分数对流方程（RSFADE）的高阶数值方法。 RSFADE是从标准的对流分散方程中获得的，它通过用$α\ in（0,1）$和$β\ in（1,2] $的riesz分数衍生物替换一阶和二阶衍生物（1,2] $）。 {f} RSFADE的差异方法。 $ \ MATHCAL {O}（τ^4+H^4）$。
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 $α\in(0,1)$ and $β\in(1,2]$, respectively. Firstly, we utilize the weighted and shifted Grünwald 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 $\mathcal {O}(τ^2+h^2)$. Thirdly, we use the Richardson extrapolation method (REM) to improve the convergence order which can be $\mathcal {O}(τ^4+h^4)$. Finally, some numerical examples are given to show the effectiveness of the numerical method, and the results are excellent with the theoretical analysis.
