Evelyn Buckwar, Markus Ableidinger,
"Weak stochastic Runge-Kutta Munthe-Kaas methods for finite spin ensembles"
, in Applied Numerical Mathematics, Vol. 118, Elsevier B.V., Seite(n) 50-63, 2017, ISSN: 0168-9274
Weak stochastic Runge-Kutta Munthe-Kaas methods for finite spin ensembles
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In this article we construct weak Runge?Kutta Munthe-Kaas methods for a finite-dimensional version of the stochastic Landau?Lifshitz equation (LL-equation). We formulate a Lie group framework for the stochastic LL-equation and derive regularity conditions for the corresponding SDE system on the Lie algebra. Using this formulation we define weak Munthe-Kaas methods based on weak stochastic Runge?Kutta methods (SRK methods) and provide sufficient conditions such that the Munthe-Kaas methods inherit the convergence order of the underlying SRK method. The constructed methods are fully explicit and preserve the norm constraint of the LL-equation exactly. Numerical simulations are provided to illustrate the convergence order as well as the long time behaviour of the proposed methods.