We introduce and analyze an explicit time discretization scheme for the one-dimensional stochastic Allen-Cahn, driven by space-time white noise. The scheme is based on a splitting strategy, and uses the exact solution for the nonlinear term contribution.
We first prove boundedness of moments of the numerical solution. We then prove strong convergence results: first, $L^2(\Omega)$-convergence of order almost $1/4$, localized on an event of arbitrarily large probability, then convergence in probability of order almost $1/4$.
The theoretical analysis is supported by numerical experiments, concerning strong and weak orders of convergence.
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Mean square error order for
Weak error order for