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

Foster, E.L.; Lohéac, Jérôme; Tran, M.-B.

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

Journal article (2017)

Authors

E.L. Foster Sandia National Laboratories, New Mexico

Jérôme Lohéac École des Mines de Nantes

M.-B. Tran University of Wisconsin-Madison

Affiliation

External organisation

Kolmogorov equation Long time simulation Self-similar variables

To reference this document use:

http://resolver.tudelft.nl/uuid:2684d58a-49e8-4971-aeff-740e0737e425

More Info

expand_more

Published Date

2017

Language

Undefined/Unknown

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Affiliation

External organisation

Abstract

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.