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 5-6 966-995

Ämneskategorier

Beräkningsmatematik

Sannolikhetsteori och statistik

Matematisk analys

DOI

10.1002/mana.201600283