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.
Author
Mihaly Kovacs
Stig Larsson
University of Gothenburg
Chalmers, Mathematical Sciences, Mathematics
Fredrik Lindgren
Subject Categories
Computational Mathematics
Probability Theory and Statistics
Roots
Basic sciences