We examine a heterogeneous alternating-direction method for the approximate solution of the FENE Fokker–Planck equation from polymer fluid dynamics and we use this method to solve a coupled (macro-micro) Navier–Stokes–Fokker–Planck system for dilute polymeric fluids. In this context the Fokker–Planck equation is posed on a high-dimensional domain and is therefore challenging from a computationa...

We present a master equation formulation based on a Markovian random walk model that exhibits subdiffusion, classical diffusion, and superdiffusion as a function of a single parameter. The nonclassical diffusive behavior is generated by allowing for interactions between a population of walkers. At the macroscopic level, this gives rise to a nonlinear Fokker-Planck equation. The diffusive behavi...

The determination of the relaxation of electrons in atomic gases continues to be an important physical problem. The main interest is the determination of the time scale for the thermalization of electrons in different moderators and the nature of the time-dependent electron energy distribution. The theoretical basis for the study of electron thermalization is the determination of the electron d...

A Langevin equation with variable drift and diffusion coefficients separable in time and space and its corresponding Fokker-Planck equation in the Stratonovich approach are considered. From this Fokker-Planck equation a class of exact solutions with the same spatial drift and diffusion coefficients is obtained. Furthermore, some details of this system are analyzed by using the spatial diffusion...

We consider the modeling of light beams propagating in highly forward-peaked turbulent media by fractional Fokker-Planck equations and their approximations Fermi pencil beam models. We obtain an error estimate a 1-Wasserstein distance for latter model showing that spreading is well captured pencil-beam approximation small diffusion limit.

This paper aims to propose a generalized fractional Fokker–Planck equation based on stable Lévy stochastic process. To develop the general equation, we will use process rather than Brownian motion. Due process, this can provide better description of heavy tails and skewness. The analytical solution is chosen solve expressed using H-function demonstrate indicator entropy production rate. We mode...

<p style='text-indent:20px;'>In this paper, we study the numerical approximation of a system PDEs which arises from an optimal control problem for time-fractional Fokker-Planck equation with time-dependent drift. The is composed backward Hamilton-Jacobi-Bellman and forward equation. We approximate Caputo derivatives in by means L1 schemes Hamiltonian finite differences. scheme constructed...

In this paper, we develop a numerical method for the L\'evy-Fokker-Planck equation with fractional diffusive scaling. There are two main challenges. One comes from two-fold nonlocality, that is, need to apply Laplacian operator power law decay distribution. The other arises long-time/small mean-free-path scaling, which introduces stiffness equation. To resolve first difficulty, use change of va...

Fractional Fokker-Planck equations FFPEs have gained much interest recently for describing transport dynamics in complex systems that are governed by anomalous diffusion and nonexponential relaxation patterns. However, effective numerical methods and analytic techniques for the FFPE are still in their embryonic state. In this paper, we consider a class of time-space fractional Fokker-Planck equ...