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New two-level leapfrog scheme for modeling the stochastic Landau-Lifshitz equations. (Russian, English) Zbl 1313.35373

Zh. Vychisl. Mat. Mat. Fiz. 54, No. 2, 298-317 (2014); translation in Comput. Math. Math. Phys. 54, No. 2, 315-334 (2014).
Summary: A two-level modification of the classical nondissipative leapfrog scheme with nonlinear flux correction has been developed for fluctuating hydrodynamics problems. The new algorithm has been shown to satisfy the fluctuation-dissipation theorem to high accuracy. The results of various numerical tests, including equilibrium, nonequilibrium, one-, and two-dimensional systems, are compared with theoretical predictions, direct molecular simulations, and results produced by MacCormack’s schemes, the piecewise parabolic method, and a third-order Runge-Kutta scheme. The new algorithm is well suited for parallel computations due to its implementation simplicity and compact stencil.

MSC:

35R60 PDEs with randomness, stochastic partial differential equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
65C30 Numerical solutions to stochastic differential and integral equations
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References:

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