In this paper, an efficient algorithm is presented by adopting the extrapolation technique to improve the accuracy of finite difference schemes for two-dimensional space-fractional diffusion equations with non-smooth solution. The popular fractional centered difference scheme is revisited and the stability and error estimation of numerical solution are given in maximum norm. Based on the analysis of leading singularity of exact solution for the underlying problem, the extrapolation technique and numerical correction method are exploited to enhance the accuracy and convergence rate of the computation. Two numerical examples are provided to validate the theoretical prediction and efficiency of the algorithm. It is shown that, by using the proposed algorithm, both accuracy and convergence rate of numerical solutions can be significantly improved and the second-order accuracy can even be recovered for the equations with large fractional orders.

本文提出了一种有效的算法，采用外推技术提高了具有非光滑解的二维空间分式扩散方程有限差分格式的精度。重新讨论了流行的分数中心差分方案，并以最大范数给出了数值解的稳定性和误差估计。在对潜在问题的精确解的前导奇异性进行分析的基础上，利用外推技术和数值校正方法来提高计算的准确性和收敛速度。提供了两个数值示例，以验证算法的理论预测和效率。结果表明，通过所提出的算法，