Analysis of splitting methods for solving a partial integro-differential

Fokker-Planck equation. Applied Mathematics and Computation, 294:1-17, 2017.

For the stochastic system (42) the

Fokker-Planck equation reads

The

Fokker-Planck equation in image space {[??]} is then given by

Stohny, "Symmetry properties and exact solutions of the

fokker-planck equation," Journal of Nonlinear Mathematical Physics, vol.

In the

Fokker-Planck equation, the so called Kramers-Moyal coefficients [D.sub.I]([alpha], t) and [D.sub.2]([alpha], t) describe drift ([D.sub.I]) and diffusion ([D.sub.2]) of the probability distribution.

The most difficult part of the code is the solution of the

Fokker-Planck equation. There are three parameters.

(i) The square-root of [B.sub.[alpha][beta]] (e.g., the Cholesky-decomposition, [b.sub.[alpha][beta]]) exists, required by the correspondence of the SDE (5) and the

Fokker-Planck equation (6).

as can be seen from inserting the rates (28) and (29) into the

Fokker-Planck equation (22).

A probability distribution function of fiber orientation (or

Fokker-Planck equation) is introduced by statistical method in concentrated suspensions.

By expanding the functions g, d, f, which depend smoothly on n, into a Taylor series to the second order inclusive, the system of the discrete equations is represented by the continual differential equation in the partial derivatives (

Fokker-Planck equation) [2]:

In 17 concise chapters and a remarkable collection of appendices be describes the Langevin equation, the fluctuation-dissipation relation, auto-correlation of velocity, Markov processes, the

Fokker-Planck equation, the diffusion equation, diffusion in a finite region, Brownian motion, first-passage time, displacement phase-space

Fokker-Planck equations, diffusion as a potential, diffusion in a magnetic field, Kubo-Green formulas, dynamic mobility, and the generalized Langevin equation.