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 - <p style="text-align: justify;">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.</p>