Compact finite difference method for the fractional diffusion equation

Cui M.

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Compact finite difference method for the fractional diffusion equation

机译：分数阶扩散方程的紧致有限差分方法

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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 Grünwald-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.

机译：考虑一维分数阶扩散方程的高阶紧致差分格式。通过紧致的有限差分近似于空间的二阶导数后，我们使用Riemann-Liouville导数的Grünwald-Letnikov离散化来获得完全离散的隐式方案。我们分析了局部截断误差并使用傅里叶方法讨论了稳定性，然后通过矩阵分析证明了紧致的有限差分格式与四阶空间精度收敛。数值结果证明了所提算法的准确性和有效性。

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来源
《Journal of Computational Physics》 |2009年第20期|共13页
作者
Cui M.;
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正文语种 eng
中图分类数学物理方法;
关键词
Compact scheme; Convergence; Finite difference; Fourier analysis; Fractional diffusion equation; Padé approximant; Stability;

机译：紧致格式;收敛;有限差分;Fourier分析;分数阶扩散方程;Padé逼近;稳定性;

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Compact finite difference method for the fractional diffusion equation

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