On the discretisation in time of the stochastic Allen-Cahn equation
Artikel i vetenskaplig tidskrift, 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
Författare
Mihaly Kovacs
Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik
University of Otago
Stig Larsson
Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik
Fredrik Lindgren
Osaka University
Mathematische Nachrichten
0025-584X (ISSN) 1522-2616 (eISSN)
Vol. 291 5-6 966-995Ämneskategorier
Beräkningsmatematik
Sannolikhetsteori och statistik
Matematisk analys
DOI
10.1002/mana.201600283