Green’s function for one-dimensional Fokker-Planck equations with exponentially dependent drift and diffusion coefficients

1990 ◽  
Vol 42 (8) ◽  
pp. 4485-4492 ◽  
Author(s):  
A. Debosscher
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Diffusion Coefficients ◽  
One Dimensional ◽  
Fokker Planck Equations ◽  
And Diffusion ◽  
Fokker Planck

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

Non-Maxwellian kinetic equations modeling the dynamics of wealth distribution

2020 ◽  
Vol 30 (04) ◽  
pp. 685-725 ◽  
Author(s):  
Giulia Furioli ◽  
Ada Pulvirenti ◽  
Elide Terraneo ◽  
Giuseppe Toscani
Keyword(s):  
Steady State ◽  
Wealth Distribution ◽  
Kinetic Equations ◽  
Planck Equation ◽  
Logarithmic Sobolev Inequality ◽  
One Dimensional ◽  
Distribution Of Wealth ◽  
Multi Agent ◽  
Fokker Planck Equations ◽  
Fokker Planck

We introduce a class of new one-dimensional linear Fokker–Planck-type equations describing the dynamics of the distribution of wealth in a multi-agent society. The equations are obtained, via a standard limiting procedure, by introducing an economically relevant variant to the kinetic model introduced in 2005 by Cordier, Pareschi and Toscani according to previous studies by Bouchaud and Mézard. The steady state of wealth predicted by these new Fokker–Planck equations remains unchanged with respect to the steady state of the original Fokker–Planck equation. However, unlike the original equation, it is proven by a new logarithmic Sobolev inequality with weight and classical entropy methods that the solution converges exponentially fast to equilibrium.

scholarly journals Acoustic scattering from a one-dimensional array; Tail-end asymptotics for efficient evaluation of the quasi-periodic Green’s function

Wave Motion ◽  
2019 ◽  
Vol 89 ◽  
pp. 232-244
Author(s):  
Georgia M. Lynott ◽  
Victoria Andrew ◽  
I. David Abrahams ◽  
Michael J. Simon ◽  
William J. Parnell ◽  
...  
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Acoustic Scattering ◽  
One Dimensional ◽  
Dimensional Array
Sign in / Sign up

Export Citation Format

Share Document