Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776621 | Applied Numerical Mathematics | 2017 | 14 Pages |
Abstract
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
M. Ableidinger, E. Buckwar,