Compact finite difference method for the fractional diffusion equation
Compact finite difference method for the fractional diffusion equation
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DOI：
10.1016/j.jcp.2009.07.021
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发表时间：
2009-11-01
影响因子：
4.1
通讯作者：
Cui, Mingrong
中科院分区：
文献类型：
--
作者：
Cui, Mingrong
研究了求解一维分数阶扩散方程的高阶紧致有限差分格式。利用紧致有限差分近似二阶导数在空间上的近似，利用Riemann-Liouville导数的Grunwald-Letnikov离散得到了一个完全离散隐式格式。利用傅里叶方法分析了局部截断误差并讨论了其稳定性，然后利用矩阵分析证明了紧致有限差分格式收敛于四阶空间精度。数值结果验证了该算法的准确性和有效性。(C) 2009爱思唯尔公司版权所有。
High-order compact finite difference scheme for solving one-dimensional fractional diffusion equation is considered in this paper. After approximating the second-order derivative with respect to space by the compact finite difference, we use the Grunwald-Letnikov discretization of the Riemann-Liouville derivative to obtain a fully discrete implicit scheme. We analyze the local truncation error and discuss the stability using the Fourier method, then we prove that the compact finite difference scheme converges with the spatial accuracy of fourth order using matrix analysis. Numerical results are provided to verify the accuracy and efficiency of the proposed algorithm. (C) 2009 Elsevier Inc. All rights reserved.