On the discretization in time of the stochastic Allen-Cahn equation
Preprint, 2015

We consider the stochastic Allen-Cahn equation perturbed by smooth additive Gaussian noise in a 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. We show that the method converges strongly with a rate O(Δt^γ) for any γ<12. By means of a perturbation argument, we also establish the strong convergence of the standard backward Euler scheme with the same rate.

Allen-Cahn equation

addi- tive noise

Stochastic partial differential equation

Euler method

strong convergence

time discretization

Wiener process

factorisation method.

Författare

Stig Larsson

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Fredrik Lindgren

Ämneskategorier

Beräkningsmatematik

Sannolikhetsteori och statistik

Fundament

Grundläggande vetenskaper