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An explicit scheme for stochastic Allen-Cahn equations with space-time white noise near the sharp interface limit
arXiv:2601.01894v1 Announce Type: new
Abstract: This article investigates time-discrete approximations of Allen-Cahn type SPDEs driven by space-time white noise near the sharp interface limit $\epsilon\to 0$, where the small parameter $\epsilon$ is the diffuse interface thickness. We propose an explicit and easily implementable exponential integrator with a modified nonlinearity for the considered problem. Uniform-in-time and uniform-in-$\epsilon$ moment bounds of the scheme are established and the convergence in total variation distance of order $O(T\cdot\text{Poly}(\epsilon^{-1})\tau^\gamma),\gamma
Abstract: This article investigates time-discrete approximations of Allen-Cahn type SPDEs driven by space-time white noise near the sharp interface limit $\epsilon\to 0$, where the small parameter $\epsilon$ is the diffuse interface thickness. We propose an explicit and easily implementable exponential integrator with a modified nonlinearity for the considered problem. Uniform-in-time and uniform-in-$\epsilon$ moment bounds of the scheme are established and the convergence in total variation distance of order $O(T\cdot\text{Poly}(\epsilon^{-1})\tau^\gamma),\gamma
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