{"title":"Upwind Bicompact Schemes for Hyperbolic Conservation Laws","authors":"M. D. Bragin","doi":"10.1134/S1064562424702089","DOIUrl":null,"url":null,"abstract":"<p>Upwind bicompact schemes of third-order approximation in space are presented for the first time. A formula is obtained for the transition factor of an arbitrary fully discrete bicompact scheme with Runge–Kutta time stepping. Stability and monotonicity of a scheme of first order in time are investigated, and the dissipative and dispersion properties of a scheme of third order in time are analyzed. Advantages of the new schemes over their centered counterparts are demonstrated.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"109 3","pages":"232 - 237"},"PeriodicalIF":0.5000,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S1064562424702089","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Upwind bicompact schemes of third-order approximation in space are presented for the first time. A formula is obtained for the transition factor of an arbitrary fully discrete bicompact scheme with Runge–Kutta time stepping. Stability and monotonicity of a scheme of first order in time are investigated, and the dissipative and dispersion properties of a scheme of third order in time are analyzed. Advantages of the new schemes over their centered counterparts are demonstrated.
期刊介绍：
Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.
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