{"title":"用于数学物理问题数值求解的新型经济无条件稳定分割法","authors":"Ek. L. Kuznetsova, O. V. Egorova, A. S. Novikov","doi":"10.1134/s1995080224602467","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, an economical unconditionally stable method of variable directions with extrapolation of numerical solutions of problems for parabolic equations containing mixed derivatives is proposed and justified by approximation and stability, which, in comparative analysis with other numerical methods, showed the highest accuracy and a unique margin of stability when changing grid characteristics.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"8 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A New Economical Unconditional Stable Splitting Method for Numerical Solution of Problems of Mathematical Physics\",\"authors\":\"Ek. L. Kuznetsova, O. V. Egorova, A. S. Novikov\",\"doi\":\"10.1134/s1995080224602467\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>In this paper, an economical unconditionally stable method of variable directions with extrapolation of numerical solutions of problems for parabolic equations containing mixed derivatives is proposed and justified by approximation and stability, which, in comparative analysis with other numerical methods, showed the highest accuracy and a unique margin of stability when changing grid characteristics.</p>\",\"PeriodicalId\":46135,\"journal\":{\"name\":\"Lobachevskii Journal of Mathematics\",\"volume\":\"8 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-08-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Lobachevskii Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1134/s1995080224602467\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lobachevskii Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995080224602467","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
A New Economical Unconditional Stable Splitting Method for Numerical Solution of Problems of Mathematical Physics
Abstract
In this paper, an economical unconditionally stable method of variable directions with extrapolation of numerical solutions of problems for parabolic equations containing mixed derivatives is proposed and justified by approximation and stability, which, in comparative analysis with other numerical methods, showed the highest accuracy and a unique margin of stability when changing grid characteristics.
期刊介绍：
Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
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