A semi-discrete scheme for the stochastic Landau-Lifshitz equation

François Alouges (1) , Anne de Bouard (1) , Antoine Hocquet (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We propose a new convergent time semi-discrete scheme for the stochastic Landau-Lifshitz-Gilbert equation. The scheme is only linearly implicit and does not require the resolution of a nonlinear problem at each time step. Using a martingale approach, we prove the convergence in law of the scheme up to a subsequence.

Mots clés: Landau-Lifshitz equation; Numerical analysis; Stochastic partial differen- tial equation

Domaines: Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]; Analyse numérique [math.NA]

François Alouges, Anne de Bouard, Antoine Hocquet. A semi-discrete scheme for the stochastic Landau-Lifshitz equation. 2014. ⟨hal-00958462⟩