From the Boltzmann equation with non-local correlations to a standard non-linear Fokker-Planck equation

Iterative methods for solving non linear Fokker-Planck equation

iterative methods for solving non linear fokker-planck equation

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, ...

Diffusive Property of the Fokker-planck-boltzmann Equation

We consider the Fokker-Planck-Boltzmann equation consisting of the Boltzmann equation with an additional diffusion term in velocity space to simulate for instance the transport in thermal bath of binary elastic collisional particles, and investigate the (macroscopic) diffusion properties of solutions in large time.