{"title":"带积分条件泊松方程的交替方向隐式解法","authors":"Olga Štikonienė, Mifodijus Sapagovas","doi":"10.3846/mma.2023.18029","DOIUrl":null,"url":null,"abstract":"In this paper, we investigate the convergence of the Peaceman-Rachford Alternating Direction Implicit method for the system of difference equations, approximating the two-dimensional elliptic equations in rectangular domain with nonlocal integral conditions. The main goal of the paper is the analysis of spectrum structure of difference eigenvalue problem with nonlocal conditions. The convergence of iterative method is proved in the case when the system of eigenvectors is complete. The main results are generalized for the system of difference equations, approximating the differential problem with truncation error O(h4).","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"ALTERNATING DIRECTION IMPLICIT METHOD FOR POISSON EQUATION WITH INTEGRAL CONDITIONS\",\"authors\":\"Olga Štikonienė, Mifodijus Sapagovas\",\"doi\":\"10.3846/mma.2023.18029\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we investigate the convergence of the Peaceman-Rachford Alternating Direction Implicit method for the system of difference equations, approximating the two-dimensional elliptic equations in rectangular domain with nonlocal integral conditions. The main goal of the paper is the analysis of spectrum structure of difference eigenvalue problem with nonlocal conditions. The convergence of iterative method is proved in the case when the system of eigenvectors is complete. The main results are generalized for the system of difference equations, approximating the differential problem with truncation error O(h4).\",\"PeriodicalId\":49861,\"journal\":{\"name\":\"Mathematical Modelling and Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2023-10-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Modelling and Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3846/mma.2023.18029\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Modelling and Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3846/mma.2023.18029","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
ALTERNATING DIRECTION IMPLICIT METHOD FOR POISSON EQUATION WITH INTEGRAL CONDITIONS
In this paper, we investigate the convergence of the Peaceman-Rachford Alternating Direction Implicit method for the system of difference equations, approximating the two-dimensional elliptic equations in rectangular domain with nonlocal integral conditions. The main goal of the paper is the analysis of spectrum structure of difference eigenvalue problem with nonlocal conditions. The convergence of iterative method is proved in the case when the system of eigenvectors is complete. The main results are generalized for the system of difference equations, approximating the differential problem with truncation error O(h4).
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