{"title":"On the Stability of a Central Difference Scheme with a Stabilizing Correction for the 3D Transport Equation","authors":"V. P. Zhukov","doi":"10.1134/s0965542524700271","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>It is generally accepted that the central differences scheme with a stabilizing correction for the transport equation in the 3D case is conditionally stable. This article shows that, strictly speaking, this scheme is absolutely unstable. However, the region of unstable harmonics in the wave vector space and their increments quickly tend to zero as the Courant parameter tends to zero, which makes it possible to successfully use this scheme. Therefore, it is more correct to talk about the practically conditional stability of this scheme.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"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/s0965542524700271","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
It is generally accepted that the central differences scheme with a stabilizing correction for the transport equation in the 3D case is conditionally stable. This article shows that, strictly speaking, this scheme is absolutely unstable. However, the region of unstable harmonics in the wave vector space and their increments quickly tend to zero as the Courant parameter tends to zero, which makes it possible to successfully use this scheme. Therefore, it is more correct to talk about the practically conditional stability of this scheme.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
