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On the discretization in time of the stochastic Allen-Cahn equation

Mihaly Kovacs ; Stig Larsson (Institutionen för matematiska vetenskaper, matematik) ; Fredrik Lindgren

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.

Nyckelord: Stochastic partial differential equation; Allen-Cahn equation; addi- tive noise; Wiener process; Euler method; time discretization; strong convergence; factorisation method.

Denna post skapades 2015-10-14.
CPL Pubid: 224161


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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)


Numerisk analys
Matematisk statistik

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