Immersed Interface Method for Fokker-Planck Equation with Discontinuous Drift

Iterative methods for solving non linear Fokker-Planck equation

The Entropy Satisfying Discontinuous Galerkin Method for Fokker-Planck equations

In Liu and Yu (SIAM J Numer Anal 50(3):1207–1239, 2012), we developed a finite volume method for Fokker–Planck equations with an application to finitely extensible nonlinear elastic dumbbell model for polymers subject to homogeneous fluids. The method preserves positivity and satisfies the discrete entropy inequalities, but has only first order accuracy in general cases. In this paper, we overc...

An Improved Wpe Method for Solving Discontinuous Fokker-planck Equations

Abstract. In mathematical studies of molecular motors, the stochastic motor motion is modeled using the Langevin equation. If we consider an ensemble of motors, the probability density is governed by the corresponding Fokker-Planck equation. Average quantities, such as, average velocity, effective diffusion and randomness parameter, can be calculated from the probability density. The WPE method...

The Fokker-Planck equation

In 1984, H. Risken authored a book (H. Risken, The Fokker-Planck Equation: Methods of Solution, Applications, Springer-Verlag, Berlin, New York) discussing the Fokker-Planck equation for one variable, several variables, methods of solution and its applications, especially dealing with laser statistics. There has been a considerable progress on the topic as well as the topic has received greater...

The Fokker-Planck Equation

Stochastic differential equations (SDE) are used to model many situations including population dynamics, protein kinetics, turbulence, finance, and engineering [5, 6, 1]. Knowing the solution of the SDE in question leads to interesting analysis of the trajectories. Most SDE are unsolvable analytically and other methods must be used to analyze properties of the stochastic process. From the SDE, ...