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Volume 10, Issue 2
Second-Order Schemes for Fokker-Planck Equations with Discontinuous Drift

Boya Zhang, Yaming Chen & Songhe Song

Adv. Appl. Math. Mech., 10 (2018), pp. 343-361.

Published online: 2018-10

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  • 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.

  • AMS Subject Headings

65M06, 65M08, 35Q84

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-10-343, author = {Zhang , BoyaChen , Yaming and Song , Songhe}, title = {Second-Order Schemes for Fokker-Planck Equations with Discontinuous Drift}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {2}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2017-0098}, url = {http://global-sci.org/intro/article_detail/aamm/12215.html} }
TY - JOUR T1 - Second-Order Schemes for Fokker-Planck Equations with Discontinuous Drift AU - Zhang , Boya AU - Chen , Yaming AU - Song , Songhe JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 343 EP - 361 PY - 2018 DA - 2018/10 SN - 10 DO - http://doi.org/10.4208/aamm.OA-2017-0098 UR - https://global-sci.org/intro/article_detail/aamm/12215.html KW - Brownian motion with dry friction, Fokker-Planck equation, discontinuous coefficient, finite volume method, alternating direction implicit method. AB -

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.

Zhang , BoyaChen , Yaming and Song , Songhe. (2018). Second-Order Schemes for Fokker-Planck Equations with Discontinuous Drift. Advances in Applied Mathematics and Mechanics. 10 (2). 343-361. doi:10.4208/aamm.OA-2017-0098
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