In this paper, we propose and analyze an explicit time-stepping scheme for a spatial discretization of stochastic Cahn-Hilliard equation with additive noise. The fully discrete approximation combines a spectral Galerkin method in space with a tamed exponential Euler method in time. In contrast to implicit schemes in the literature, the explicit scheme here is easily implementable and produces significant improvement in the computational efficiency. It is shown that the fully discrete approximation converges strongly to the exact solution, with strong convergence rates identified. To the best of our knowledge, it is the first result concerning an explicit scheme for the stochastic Cahn-Hilliard equation. Numerical experiments are finally performed to confirm the theoretical results.

翻译：在本文中,我们提出并分析一个明确的时间步骤计划,用添加噪音将零碎的卡赫恩-希利亚德方程式的空间分解。完全离散近光线将空间的光谱加列金法与及时的驯服指数极速法相结合。与文献中的隐含计划相比,此处的清晰计划易于实施,并极大地提高了计算效率。这表明完全离散的近光线与确切的解决方案紧密相联,并确定了很强的趋同率。据我们所知,这是关于光谱卡赫恩-希利亚德方程式的明确计划的第一个结果。最终进行了数字实验,以证实理论结果。