Numerical solutions of Fokker-Planck equations with drift-admitting jumps
arXiv:1808.10815 · doi:10.1103/PhysRevE.98.033302
Abstract
We develop a finite difference scheme based on a grid staggered by flux points and solution points to solve Fokker-Planck equations with drift-admitting jumps. To satisfy the matching conditions at the jumps, i.e., the continuities of the propagator and the probability current, the jumps are set to be solution points and used to divide the solution domain into subdomains. While the values of the probability current at flux points are obtained within each subdomain, the values of its first derivative at solution points are evaluated by using stencils across the subdomains. Several benchmark problems are solved numerically to show the validity of the proposed scheme.
References in corpus (22)
- Brownian motors: noisy transport far from equilibrium
- A unified approach for the solution of the Fokker-Planck equation
- Brownian motion with dry friction: Fokker-Planck approach
- Structure preserving schemes for nonlinear Fokker-Planck equations and applications
- Langevin equation with Coulomb friction
- A Numerical Method for SDEs with Discontinuous Drift
- Stick-slip motion of solids with dry friction subject to random vibrations and an external field
- Non-Gaussian Velocity Distribution Function in a Vibrating Granular Bed
- The effect of Coulombic friction on spatial displacement statistics
- Singular features in noise-induced transport with dry friction
- Path integral approach to random motion with nonlinear friction
- Weak-noise limit of a piecewise-smooth stochastic differential equation
- Exact power spectra of Brownian motion with solid friction
- Roles of Dry Friction in Fluctuating Motion of Adiabatic Piston
- Rectification of asymmetric surface vibrations with dry friction: an exactly solvable model
- Nonequilibrium dynamics of a pure dry friction model subjected to coloured noise
- First-passage time of Brownian motion with dry friction
- Granular rotor as a probe for a non-equilibrium bath
- On large deviation properties of Brownian motion with dry friction
- Single Particle Brownian Motion with Solid Friction
- Exact sampling of diffusions with a discontinuity in the drift
- On energy dissipation in a friction-controlled slide of a body excited by random motions of the foundation