In this paper we propose an explicit fully discrete scheme to numerically solve the stochastic Allen-Cahn equation. The spatial discretization is done by a spectral Galerkin method, followed by the temporal discretization by a tamed accelerated exponential Euler scheme. Based on the time-independent boundedness of moments of numerical solutions, we present the weak error analysis in an infinite time interval by using Malliavin calculus. This provides a way to numerically approximate the invariant measure for the stochastic Allen-Cahn equation.

翻译：本文提出一种显式全离散格式用于数值求解随机Allen-Cahn方程。空间离散采用谱Galerkin方法实现，随后通过驯服加速指数欧拉格式进行时间离散。基于数值解矩的时无关有界性，我们运用Malliavin分析在无限时间区间上给出了弱误差分析。这为数值逼近随机Allen-Cahn方程的不变测度提供了一种途径。