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arXiv · 1801.06455

Analysis of Some Splitting Schemes for the Stochastic Allen-Cahn Equation

Charles-Edouard Bréhier·Ludovic Goudenège
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Abstract

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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Charles-Edouard Bréhier, Ludovic Goudenège. 2018-01-19. Analysis of Some Splitting Schemes for the Stochastic Allen-Cahn Equation. https://doi.org/10.3934/dcdsb.2019077

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