TY - JOUR

T1 - Study and Optimization of N-Particle Numerical Statistical Algorithm for Solving the Boltzmann Equation

AU - Lotova, G. Z.

AU - Mikhailov, G. A.

AU - Rogasinsky, S. V.

PY - 2024/5

Y1 - 2024/5

N2 - Abstract: The main goal of this work is to check the hypothesis that the well-known N-particle statistical algorithm yields a solution estimate for the nonlinear Boltzmann equation with an error. For this purpose, practically important optimal relations between and the number of sample estimate values are determined. Numerical results for a problem with a known solution confirm that the formulated estimates and conclusions are satisfactory.

AB - Abstract: The main goal of this work is to check the hypothesis that the well-known N-particle statistical algorithm yields a solution estimate for the nonlinear Boltzmann equation with an error. For this purpose, practically important optimal relations between and the number of sample estimate values are determined. Numerical results for a problem with a known solution confirm that the formulated estimates and conclusions are satisfactory.

KW - Boltzmann equation

KW - Monte Carlo method

KW - N-particle Markov chain

KW - majorizing frequency method

KW - molecular chaos

KW - statistical modeling

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85196121994&origin=inward&txGid=be3cc2aa598e39343b239aa38f8b0c72

UR - https://www.mendeley.com/catalogue/a4e8d3d9-1000-34f4-ab0f-281d9ba67353/

U2 - 10.1134/S0965542524700246

DO - 10.1134/S0965542524700246

M3 - Article

VL - 64

SP - 1065

EP - 1075

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 5

ER -