{"title":"Study and Optimization of N-Particle Numerical Statistical Algorithm for Solving the Boltzmann Equation","authors":"G. Z. Lotova, G. A. Mikhailov, S. V. Rogasinsky","doi":"10.1134/s0965542524700246","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The main goal of this work is to check the hypothesis that the well-known <i>N</i>-particle statistical algorithm yields a solution estimate for the nonlinear Boltzmann equation with an <span>\\(O(1{\\text{/}}N)\\)</span> error. For this purpose, practically important optimal relations between <span>\\(N\\)</span> and the number <span>\\(n\\)</span> of sample estimate values are determined. Numerical results for a problem with a known solution confirm that the formulated estimates and conclusions are satisfactory.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":"7 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Mathematics and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0965542524700246","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
Computational Mathematics and Mathematical Physics is a monthly journal published in collaboration with the Russian Academy of Sciences. The journal includes reviews and original papers on computational mathematics, computational methods of mathematical physics, informatics, and other mathematical sciences. The journal welcomes reviews and original articles from all countries in the English or Russian language.
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