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Journal Articles Journal of Computational Physics Year : 2017

A Structure Preserving Scheme for the Kolmogorov-Fokker-Planck Equation

Abstract

In this paper we introduce a numerical scheme which preserves the long time behavior of solutions to the Kolmogorov equation. 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. We also present an analysis for the operator splitting technique for the self-similar method and numerical results for the described scheme.
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Dates and versions

hal-01493646 , version 1 (16-05-2024)

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Erich L Foster, Jérôme Lohéac, Minh-Binh Tran. A Structure Preserving Scheme for the Kolmogorov-Fokker-Planck Equation. Journal of Computational Physics, 2017, 330, pp.319 - 339. ⟨10.1016/j.jcp.2016.11.009⟩. ⟨hal-01493646⟩
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