A Structure Preserving Scheme for the Kolmogorov-Fokker-Planck Equation
Numerical Analysis
2014-11-06 v2
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.
Keywords
Cite
@article{arxiv.1411.1019,
title = {A Structure Preserving Scheme for the Kolmogorov-Fokker-Planck Equation},
author = {Erich L Foster and Jérôme Lohéac and Minh-Binh Tran},
journal= {arXiv preprint arXiv:1411.1019},
year = {2014}
}