{"title":"Error analysis of Fourier-Legendre and Fourier-Hermite spectral-Galerkin methods for the Vlasov-Poisson system","authors":"XIAOLONG ZHANG, Li-Lian Wang, HONGLI JIA","doi":"10.1051/m2an/2023091","DOIUrl":null,"url":null,"abstract":"We conduct a rigorous error analysis of the spectral-Galerkin methods for the 1D1V Vlasov-Poisson system with the velocity variable in both a finite or an infinite domain. The estimates significantly improve the very limited existing results. We also provide numerical results to demonstrate the effectiveness of the analysed methods.","PeriodicalId":51249,"journal":{"name":"Esaim-Probability and Statistics","volume":"4 10","pages":"0"},"PeriodicalIF":0.6000,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Probability and Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1051/m2an/2023091","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
We conduct a rigorous error analysis of the spectral-Galerkin methods for the 1D1V Vlasov-Poisson system with the velocity variable in both a finite or an infinite domain. The estimates significantly improve the very limited existing results. We also provide numerical results to demonstrate the effectiveness of the analysed methods.
期刊介绍：
The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains.
Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics.
Long papers are very welcome.
Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.
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