Second-Order Schemes for Fokker-Planck Equations with Discontinuous Drift

Second-Order Schemes for Fokker-Planck Equations with Discontinuous Drift

Year:    2018

Author:    Boya Zhang, Yaming Chen, Songhe Song

Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 2 : pp. 343–361

Abstract

Second-order finite-difference schemes are developed to solve the corresponding Fokker-Planck equation of Brownian motion with dry friction, which is one of the simplest models of stochastic piecewise-smooth systems. For the Fokker-Planck equation with a discontinuous drift, both explicit and implicit second order schemes are derived by finite volume method. The proposed schemes are proved to be stable both for the one-variable (related to the velocity only) and two-variable (related to the velocity and displacement) cases. Numerical experiments are implemented for both the two cases. Some known analytical results of the considered model are used to confirm the effectiveness and desired accuracy of the schemes.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2017-0098

Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 2 : pp. 343–361

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Brownian motion with dry friction Fokker-Planck equation discontinuous coefficient finite volume method alternating direction implicit method.

Author Details

Boya Zhang

Yaming Chen

Songhe Song

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