The space fractional Cahn–Hilliard phase-field model is more adequate and accurate in the description of the formation and phase change mechanism than the classical Cahn–Hilliard model. In this article, we propose a temporal second-order energy stable scheme for the space fractional Cahn–Hilliard model. The scheme is based on the second-order backward differentiation formula in time and a finite difference method in space. Energy stability and convergence of the scheme are analyzed, and the optimal convergence orders in time and space are illustrated numerically. Note that the coefficient matrix of the scheme is a \(2 \times 2\) block matrix with a Toeplitz-like structure in each block. Combining the advantages of this special structure with a Krylov subspace method, a preconditioning technique is designed to solve the system efficiently. Numerical examples are reported to illustrate the performance of the preconditioned iteration.

与经典的Cahn-Hilliard模型相比，空间分数Cahn-Hilliard相场模型在描述形成和相变机理方面更充分，更准确。在本文中，我们为空间分数Cahn-Hilliard模型提出了一个时间二阶能量稳定方案。该方案基于时间上的二阶后向微分公式和空间上的有限差分法。分析了该方案的能量稳定性和收敛性，并给出了时间和空间上的最优收敛阶数。请注意，该方案的系数矩阵为\（2 \ times 2 \）每个块中具有类似Toeplitz结构的块矩阵。结合这种特殊结构的优点和Krylov子空间方法，设计了一种预处理技术来有效地解决系统问题。报告了数值示例，以说明预处理迭代的性能。