The current paper proposes a new high-order finite difference scheme with low computational complexity to solve the space-time fractional tempered diffusion equation. At the first stage, the time derivative has been approximated by a difference scheme with second-order accuracy. Furthermore, in the next step, a compact operator has been employed to discretize the space derivative with fourth-order accuracy. After deriving the time-discrete scheme, its stability is analysed. So, a suitable term is added to the main difference scheme. By adding this term, we could construct the main ADI scheme. In the final stage, the convergence order of the full-discrete scheme based upon the ADI formulation is proved. The convergence order of the constructed technique is $\mathcal{O}((h_x^{\alpha }{)}^4+(h_y^{\beta }{)}^4+{\tau }^2)$. The numerical results show the efficiency of the new technique.

本论文提出了一种新的低计算复杂度的高阶有限差分格式来求解时空分数回火扩散方程。在第一阶段，时间导数已通过具有二阶精度的差分格式近似。此外，在下一步中，已采用紧凑算子以四阶精度离散空间导数。推导出时间离散方案后，对其稳定性进行分析。因此，一个合适的项被添加到主差分方案中。通过添加该术语，我们可以构建主要的 ADI 方案。在最后阶段，证明了基于 ADI 公式的全离散方案的收敛顺序。构造技术的收敛阶数为$\mathcal{哦}((H_X^{\alpha }{)}^4+(H_{是}^{\beta }{)}^4+{\tau }^2)$. 数值结果显示了新技术的有效性。