Convergence with rates for a time-discretization of the Stochastic Landau-Lifschitz-Gilbert equation

Abstract

Convergence in probability with rate of order ½ for finite times for a time-discretized scheme to approximate the stochastic Landau–Lifschitz–Gilbert equation is shown. The scheme is based on the midpoint rule, which preserves the sphere constraint. Computational studies provided in this work support this convergence rate.