In this paper, a high-order compact finite difference method (CFDM) with an operator-splitting technique for solving the 3D time-fractional diffusion equation is considered. The Caputo–Fabrizio time operator is evaluated by the \(L_1\) approximation, and the second-order space derivatives are approximated by the compact CFDM to obtain a discrete scheme. Alternating direction implicit method (ADI) is used to split the problem into three separate one-dimensional problems. The local truncation error analysis is discussed. Moreover, the convergence and stability of the numerical method are investigated. Finally, some numerical examples are presented to demonstrate the accuracy of the compact ADI method.

在本文中，考虑了使用算子分解技术的高阶紧致有限差分法（CFDM），用于求解3D时间分数扩散方程。Caputo–Fabrizio时间算子通过\（L_1 \）近似求值，而二阶空间导数通过紧凑CFDM近似得到离散方案。交替方向隐式方法（ADI）用于将问题分解为三个单独的一维问题。讨论了局部截断误差分析。此外，研究了数值方法的收敛性和稳定性。最后，给出了一些数值例子来说明紧凑型ADI方法的准确性。