On the discretisation in time of the stochastic Allen-Cahn equation
Journal article, 2018

We consider the stochastic Allen–Cahn equation perturbed by smooth additive Gaussian noise in a bounded spatial domain with smooth boundary in dimension d≤3, and study the semidiscretisation in time of the equation by an Euler type split-step method with step size k > 0. We show that the method converges strongly with a rate O(k 1/2 . By means of a perturbation argument, we also establish the strong convergence of the standard backward Euler scheme with the same rate.


splitting method

Additive noise

Euler method

Allen–Cahn equation


stochastic partial differential equation

Wiener process


time discretisation

strong convergence


Mihaly Kovacs

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Otago

Stig Larsson

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Fredrik Lindgren

Osaka University

Mathematische Nachrichten

0025-584X (ISSN) 1522-2616 (eISSN)

Vol. 291 5-6 966-995

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Mathematical Analysis



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