A structure preserving scheme for the Kolmogorov-Fokker-Planck equation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:330

Article

Foster, Erich L.¹  Loheac, Jerome²  Minh-Binh Tran³ 

[1] Sandia Natl Labs, Ctr Res Comp, POB 5800, Albuquerque, NM 87185 USA

[2] LUNAM Univ, IRCCyN UMR CNRS 6597, Ecole Mines Nantes, Inst Rech Commun & Cybernet Nantes, 4 Rue Alfred Kastler, F-44307 Nantes, France

[3] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

关键词: Kolmogorov equation;    Long time simulation;    Self-similar variables;   

DOI  :  10.1016/j.jcp.2016.11.009

来源: Elsevier

【 摘 要 】

In this paper we introduce a numerical scheme which preserves the behavior of solutions to the Kolmogorov Equation as time tends to infinity. The method presented is based on a self-similar change of variables technique to transform the Kolmogorov Equation into a new form, such that the problem of designing structure preserving schemes, for the original equation, amounts to building a standard scheme for the transformed equation. This transformation also has the added benefit of allowing for an exact operator splitting scheme, whereas in the original form a standard operator splitting was only second-order. Finally, we verify the preservation of long time behavior through numerical simulations. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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