Математическое моделирование, компьютерный и натурный эксперимент в естественных науках
Электронный научный журнал

Физико-математические науки
Application of Kinetic Models and Simulation of Multi-particle Systems in Some Fields of Science
Burmistrov A.V. 1, 2, Burmistrov A.V. 1, 2, Korotchenko M.A. 2

1. Novosibirsk State University
2. Institute of Computational Mathematics and Mathematical Geophysics SB RAS

Abstract:

In this paper we cover our experience applied in the field of multi-particle systems simulation for some problems arising in various fields of science such as rarefied gas dynamics, particle coagulation, vehicular traffic flows, and price formation. All these problems are described by the Boltzmann type equations. To solve them numerically, we apply the approach which uses the integral equation of the second kind and the corresponding Markov chain. The latter is uniquely determined by the coefficients of the integral equation. It allows spreading the well-developed theory of weight Monte Carlo methods to the considered problems.

Keywords: Monte Carlo method, multi-particle system evolution, pairwise interactions, coagulation equation, vehicular traffic flow, price formation

Сайт работает на RAE Editorial System