A weighted finite difference method for the fractional diffusion equation based on the Riemann-Liouville derivative
A weighted finite difference method for the fractional diffusion equation based on the Riemann-Liouville derivative
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DOI：
10.1016/j.apnum.2014.11.007
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发表时间：
2011-09
影响因子：
2.8
通讯作者：
E. Sousa;Can Li
中科院分区：
文献类型：
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作者：
E. Sousa;Can Li
研究了一类具有Riemann-Liouville分数导数的一维分数阶扩散模型。首先给出了该导数的二阶离散化，然后导出了一个无条件稳定的加权平均有限差分法。通过von Neumann分析证明了该格式的稳定性。文中给出了一些数值结果，证明了该方法的有效性和收敛性。此外，还对该分数阶扩散系统的一些物理性质进行了模拟，进一步证实了该方法的有效性。
A one dimensional fractional diffusion model with the Riemann–Liouville fractional derivative is studied. First, a second order discretization for this derivative is presented and then an unconditionally stable weighted average finite difference method is derived. The stability of this scheme is established by von Neumann analysis. Some numerical results are shown, which demonstrate the efficiency and convergence of the method. Additionally, some physical properties of this fractional diffusion system are simulated, which further confirm the effectiveness of our method.