Approximation of the invariant measure for stochastic Allen-Cahn equation via an explicit fully discrete scheme
<|reference_start|>Approximation of the invariant measure for stochastic Allen-Cahn equation via an explicit fully discrete scheme: 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.<|reference_end|>
@article{wang2024approximation,
    title={Approximation of the invariant measure for stochastic Allen-Cahn
  equation via an explicit fully discrete scheme},
    author={Yibo Wang and Wanrong Cao},
    journal={arXiv preprint arXiv:2408.00953},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.00953},
    primaryClass={math.NA cs.NA}
}