Abstract In this paper, a number of energy stable numerical schemes are proposed for the fractional Cahn–Hilliard equation. We prove mass conservation, unique solvability and energy stability for three time semi-discretized schemes based on the first-order semi-implicit scheme, the Crank–Nicolson scheme and the BDF2 scheme respectively. Then we present error analysis for these numerical schemes with the Fourier spectral approximation in space. Some numerical experiments are finally carried out to confirm accuracy and effectiveness of these proposed methods.

中文翻译：

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空间分数 Cahn-Hilliard 方程的能量稳定数值格式

摘要 本文提出了分数阶Cahn-Hilliard方程的多种能量稳定数值格式。我们分别证明了基于一阶半隐式方案、Crank-Nicolson 方案和 BDF2 方案的三个时间半离散方案的质量守恒、唯一可解性和能量稳定性。然后我们用空间中的傅立叶谱近似对这些数值方案进行误差分析。最后进行了一些数值实验，以确认这些提出的方法的准确性和有效性。