Interval Wavelet Numerical Method on Fokker-Planck Equations for Nonlinear Random System

Numerical method for the nonlinear Fokker-Planck equation

A practical method based on distributed approximating functionals ~DAFs! is proposed for numerically solving a general class of nonlinear time-dependent Fokker-Planck equations. The method relies on a numerical scheme that couples the usual path-integral concept to the DAF idea. The high accuracy and reliability of the method are illustrated by applying it to an exactly solvable nonlinear Fokke...

Random Walks Associated with Nonlinear Fokker-Planck Equations

A nonlinear random walk related to the porous medium equation (nonlinear Fokker–Planck equation) is investigated. This random walk is such that when the number of steps is sufficiently large, the probability of finding the walker in a certain position after taking a determined number of steps approximates to a q-Gaussian distribution (Gq,β(x) ∝ [1− (1− q)βx2]1/(1−q)), which is a solution of the...

Probabilistic representation for solutions to nonlinear Fokker–Planck equations

One obtains a probabilistic representation for the entropic generalized solutions to a nonlinear Fokker–Planck equation in Rd with multivalued nonlinear diffusion term as density probabilities of solutions to a nonlinear stochastic differential equation. The case of a nonlinear Fokker–Planck equation with linear space dependent drift is also studied.

1D nonlinear Fokker-Planck equations for fermions and bosons

ICREA (Institució Catalana de Recerca i Estudis Avançats) and Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain; Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain; Dipartamento di Matematica, Università degli Studi di Pavia, via Ferrata 1, I-27100 Pavia, Italy [[email protected]; [email protected]; francesco.salv...

Hurst exponents for interacting random walkers obeying nonlinear Fokker–Planck equations