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arXiv · 1510.03684

On the discretisation in time of the stochastic Allen-Cahn equation

Mihály Kovács·Stig Larsson·Fredrik Lindgren
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Abstract

We consider the stochastic Allen--Cahn equation perturbed by smooth additive Gaussian noise in a spatial domain with smooth boundary in dimension $d\le 3$, and study the semidiscretisation in time of the equation by an Euler type split-step method. We show that the method converges strongly with a rate $O(Δt^{\frac12}) $. By means of a perturbation argument, we also establish the strong convergence of the standard backward Euler scheme with the same rate.

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Mihály Kovács, Stig Larsson, Fredrik Lindgren. 2018-01-02. On the discretisation in time of the stochastic Allen-Cahn equation. https://doi.org/10.1002/mana.201600283

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