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.
60H35
splitting method
Additive noise
Euler method
Allen–Cahn equation
60H15
stochastic partial differential equation
Wiener process
65C30
time discretisation
strong convergence
Author
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 5-6 966-995Subject Categories
Computational Mathematics
Probability Theory and Statistics
Mathematical Analysis
DOI
10.1002/mana.201600283