A New Fifth-Order Finite Difference Compact Reconstruction Unequal-Sized WENO Scheme for Fractional Differential Equations
A New Fifth-Order Finite Difference Compact Reconstruction Unequal-Sized WENO Scheme for Fractional Differential Equations
复制标题
分数阶微分方程五阶有限差分紧重构不等尺寸WENO格式
DOI：
10.3390/fractalfract6060294
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发表时间：
2022-05
影响因子：
5.4
通讯作者：
Jun Zhu
中科院分区：
文献类型：
--
作者：
Yan Zhang;Jun Zhu
This paper designs a new finite difference compact reconstruction unequal-sized weighted essentially nonoscillatory scheme (CRUS-WENO) for solving fractional differential equations containing the fractional Laplacian operator. This new CRUS-WENO scheme uses stencils of different sizes to achieve fifth-order accuracy in smooth regions and maintain nonoscillatory properties near discontinuities. The fractional Laplacian operator of order β(0<β<1) is split into the integral part and the first derivative term. Using the Gauss–Jacobi quadrature method to solve the integral part of the fractional Laplacian operators, a new finite difference CRUS-WENO scheme is presented to discretize the first derivative term of the fractional equation. This new CRUS-WENO scheme has the advantages of a narrower large stencil and high spectral resolution. In addition, the linear weights of the new CRUS-WENO scheme can be any positive numbers whose sum is one, which greatly reduces the calculation cost. Some numerical examples are given to show the effectiveness and feasibility of this new CRUS-WENO scheme in solving fractional equations containing the fractional Laplacian operator.
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DOI：
10.1016/j.jcp.2019.108873
发表时间：
2019-11
期刊：
J. Comput. Phys.
影响因子：
--
作者：
Yufeng Shi;Yan Guo
通讯作者：
Yufeng Shi;Yan Guo
影响因子：
2.9
作者：
Kaur, Lakhveer;Wazwaz, Abdul-Majid
通讯作者：
Wazwaz, Abdul-Majid
DOI：
--
发表时间：
2007-09
期刊：
arXiv: Analysis of PDEs
影响因子：
--
作者：
Nathael Alibaud;P. Azérad;D. Isebe
通讯作者：
Nathael Alibaud;P. Azérad;D. Isebe
DOI：
10.1080/10618560108970024
发表时间：
2001-10
影响因子：
1.3
作者：
Li Jiang;H. Shan;Chaoqun Liu
通讯作者：
Li Jiang;H. Shan;Chaoqun Liu
影响因子：
4.1
作者：
Jiang, GS;Shu, CW
通讯作者：
Shu, CW