scholarly journals Asymptotic Solutions of the Nonlinear Boltzmann Equation for Dissipative Systems

2003 ◽  
pp. 3-36 ◽  
Author(s):  
Matthieu H. Ernst ◽  
Ricardo Brito
Keyword(s):  
Boltzmann Equation ◽  
Asymptotic Solutions ◽  
Dissipative Systems ◽  
Nonlinear Boltzmann Equation

The solution of nonlinear Boltzmann equation with an external force

2001 ◽  
Vol 12 (8) ◽  
pp. 1385-1391 ◽  
Author(s):  
S.A. El-Wakil ◽  
A. Elhanbaly ◽  
A. Elgarayhi
Keyword(s):  
Boltzmann Equation ◽  
External Force ◽  
Nonlinear Boltzmann Equation

Two variants of Monte Carlo projection method for numerical solution of nonlinear Boltzmann equation

2019 ◽  
Vol 34 (3) ◽  
pp. 143-150
Author(s):  
Sergey V. Rogasinsky
Keyword(s):  
Boltzmann Equation ◽  
Projection Method ◽  
Orthonormal Basis ◽  
Statistical Modelling ◽  
Hermite Functions ◽  
Nonlinear Boltzmann Equation ◽  
Kinetic Boltzmann Equation ◽  
Relaxation Problem ◽  
Nonlinear Kinetic ◽  
Approximation Of A Function

Abstract The paper is focused on justification of a statistical modelling algorithm for solution of the nonlinear kinetic Boltzmann equation on the base of a projection method. Hermite functions are used as an orthonormal basis. The error of approximation of a function by a partial sum of Hermite functions series is estimated in the L2 norm. The estimates are compared for two variants of the projection method in the case of solutions to the homogeneous gas relaxation problem with a known solution.

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