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
Mihaly Kovacs
Stig Larsson
Göteborgs universitet
Chalmers, Matematiska vetenskaper, Matematik
Fredrik Lindgren
Ämneskategorier
Beräkningsmatematik
Sannolikhetsteori och statistik
Fundament
Grundläggande vetenskaper