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- W2587052790 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." @default.
- W2587052790 created "2017-02-17" @default.
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- W2587052790 date "2017-08-01" @default.
- W2587052790 modified "2023-10-02" @default.
- W2587052790 title "Weak stochastic Runge–Kutta Munthe-Kaas methods for finite spin ensembles" @default.
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- W2587052790 doi "https://doi.org/10.1016/j.apnum.2017.01.017" @default.
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