Stochastic Fokker-Planck equation in random environments.

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...

Iterative methods for solving non linear Fokker-Planck equation

Generalized Fokker-Planck equation: Derivation and exact solutions

We derive the generalized Fokker-Planck equation associated with the Langevin equation (in the Ito sense) for an overdamped particle in an external potential driven by multiplicative noise with an arbitrary distribution of the increments of the noise generating process. We explicitly consider this equation for various specific types of noises, including Poisson white noise and Lévy stable noise...

Stochastic Gradient Hamiltonian Monte Carlo

Supplementary Material A. Background on Fokker-Planck Equation The Fokker-Planck equation (FPE) associated with a given stochastic differential equation (SDE) describes the time evolution of the distribution on the random variables under the specified stochastic dynamics. For example, consider the SDE: dz = g(z)dt+N (0, 2D(z)dt), (16) where z ∈ R, g(z) ∈ R, D(z) ∈ Rn×n. The distribution of z go...

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.