A second-order compact difference scheme for the fourth-order fractional sub-diffusion equation
A second-order compact difference scheme for the fourth-order fractional sub-diffusion equation
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DOI：
10.1007/s11075-017-0271-7
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发表时间：
2017-01
影响因子：
2.1
通讯作者：
Pu Zhang;H. Pu
中科院分区：
文献类型：
--
作者：
Pu Zhang;H. Pu
本文给出了一个收敛阶为o （τ2+h4）的四阶分数次扩散方程的紧致差分格式，其中τ分别为空间步长和时间步长。该方法采用theL2−1σ公式近似时间卡普托分数阶导数，采用紧算子近似空间四阶导数。利用fl2−1σ公式的特殊性质和数学归纳法，用离散能量法得到了该方案的无条件稳定性和收敛性。此外，还考虑了二维情况下的推广。数值算例验证了新方案的理论分析和有效性。
In the present work, a compact difference scheme with convergence orderO(τ2+h4) is proposed for the fourth-order fractional sub-diffusion equation, wherehandτare space and temporal step length, respectively. The method is based on applying theL2−1σformula to approximate the time Caputo fractional derivative and employing compact operator to approximate the spatial fourth-order derivative. Using the special properties ofL2−1σformula and mathematical induction method, we obtain the unconditional stability and convergence for our scheme by discrete energy method. Furthermore, the extension to the two-dimensional case is also considered. Numerical examples are given to verify the theoretical analysis and efficiency of the new developed scheme.