Geodesic
New two-level leapfrog scheme for modeling the stochastic Landau–Lifshitz equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 2, pp. 298-317 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 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. 
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     title = {New two-level leapfrog scheme for modeling the stochastic {Landau{\textendash}Lifshitz} equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     year = {2014},
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     language = {ru},
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V. Yu. Glotov; V. M. Goloviznin; S. A. Karabasov; A. P. Markeshteijn. New two-level leapfrog scheme for modeling the stochastic Landau–Lifshitz equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 2, pp. 298-317. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_2_a8/

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