求解玻尔兹曼方程的 N 粒子数值统计算法的研究与优化

Pub Date : 2024-06-13 DOI:10.1134/s0965542524700246

G. Z. Lotova, G. A. Mikhailov, S. V. Rogasinsky

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引用次数: 0

摘要

摘要这项工作的主要目的是检验一个假设，即众所周知的N粒子统计算法可以得到误差为\(O(1{text{/}}N)\)的非线性玻尔兹曼方程的解估计值。为此，确定了 \(N\) 与样本估计值数量 \(n\) 之间的重要最优关系。一个已知解问题的数值结果证实了所提出的估计和结论是令人满意的。

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

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 \(O(1{\text{/}}N)\) error. For this purpose, practically important optimal relations between \(N\) and the number \(n\) of sample estimate values are determined. Numerical results for a problem with a known solution confirm that the formulated estimates and conclusions are satisfactory.

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