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

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.

References in corpus (3)

• Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations
• On strong $L^2$ convergence of time numerical schemes for the stochastic 2D Navier-Stokes equations
• Strong convergence for explicit space-time discrete numerical approximation methods for stochastic Burgers equations

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