A compact finite difference scheme for the fourth‐order time‐fractional integro‐differential equation with a weakly singular kernel
A compact finite difference scheme for the fourth‐order time‐fractional integro‐differential equation with a weakly singular kernel
复制标题
DOI：
10.1002/num.22436
复制
发表时间：
2019-11
影响因子：
3.9
通讯作者：
Da Xu;W. Qiu;Jing Guo
中科院分区：
文献类型：
--
作者：
Da Xu;W. Qiu;Jing Guo
本文构造并研究了具有弱奇异核的四阶时间分数阶积分微分方程的紧致差分格式.在时间方向上，Caputo导数项通过L1离散公式处理，Riemann-Liouville分数积分项通过二阶卷积求积规则离散。利用四阶紧致逼近的空间离散方法构造了一个全离散的紧致差分格式。利用离散能量法、Cholesky分解和降阶方法证明了该方法的稳定性和收敛性。数值实验验证了理论分析的正确性。
In this paper, a compact finite difference scheme is constructed and investigated for the fourth‐order time‐fractional integro‐differential equation with a weakly singular kernel. In the temporal direction, the Caputo derivative term is treated by means of L1 discrete formula and the Riemann–Liouville fractional integral term is discretized by the second‐order convolution quadrature rule. A fully discrete compact difference scheme is constructed with the space discretization by the fourth‐order compact approximation. The stability and convergence are obtained by the discrete energy method, the Cholesky decomposition and the reduced‐order method. Numerical experiments are presented to verify the theoretical analysis.