Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum

How to solve Fokker-Planck equation treating mixed eigenvalue spectrum?

An analogy of the Fokker-Planck equation (FPE) with the Schrödinger equation allows us to use quantum mechanics technique to find the analytical solution of the FPE in a number of cases. However, previous studies have been limited to the Schrödinger potential with a discrete eigenvalue spectrum. Here, we will show how this approach can be also applied to a mixed eigenvalue spectrumwith bounded ...

Pseudo-spectral ‎M‎atrix and Normalized Grunwald Approximation for Numerical Solution of Time Fractional Fokker-Planck Equation

This paper presents a new numerical method to solve time fractional Fokker-Planck equation. The space dimension is discretized to the Gauss-Lobatto points, then we apply pseudo-spectral successive integration matrix for this dimension. This approach shows that with less number of points, we can approximate the solution with more accuracy. The numerical results of the examples are displayed.

Numerical Studies and Simulation of the Lower Hybrid Waves Current Drive by using Fokker – Planck Equation in NSST and HT-7 Tokamaks

Recent experiments on the spherical tokamak have discovered the conditions to create a powerful plasma and ensure easy shaping and amplification of stability, high bootstrap current and confinement energy. The spherical tours (ST) fusion energy development path is complementary to the tokamak burning plasma experiment such as NSTX and higher toroidal beta regimes and improves the design of a po...

On the master equation approach: linear and nonlinear Fokker–Planck equations

We discuss the relationship between kinetic equations of the Fokker-Planck type (two linear and one non-linear) and the Kolmogorov (a.k.a. master) equations of certain N -body diffusion processes, in the context of Kac’s propagation-of-chaos limit. The linear Fokker-Planck equations are well-known, but here they are derived as a limit N → ∞ of a simple linear diffusion equation on 3N − C-dimens...

Iterative methods for solving non linear Fokker-Planck equation