论文标题
用于二维Riesz空间分数对流分散方程的高阶数值方法
High-order numerical method for two-dimensional Riesz space fractional advection-dispersion equation
论文作者
论文摘要
在本文中，通过将分数中心差异方法与交替方向隐式方法相结合，我们引入了一种混合差异方法，用于求解二维Riesz空间分数对流 - 分散方程。所提出的方法是在空间方向上的第四阶中心差异操作员，沿时间方向二阶曲柄 - 尼科尔森方法。通过回顾该方法的一致性和稳定性，可以实现所提出的方法的收敛性。几个数值示例被认为是旨在证明所提出技术的有效性和适用性。
In this paper, by combining of fractional centered difference approach with alternating direction implicit method, we introduce a mixed difference method for solving two-dimensional Riesz space fractional advection-dispersion equation. The proposed method is a fourth order centered difference operator in spatial directions and second order Crank-Nicolson method in temporal direction. By reviewing the consistency and stability of the method, the convergence of the proposed method is achieved. Several numerical examples are considered aiming to demonstrate the validity and applicability of the proposed technique.
