有记忆的双曲型混合问题的隐式差分方案

IF 0.8 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics Pub Date : 2024-05-14 DOI:10.1134/s1995080224600249

Zh. A. Abdiramanov, Zh. D. Baishemirov, A. S. Berdyshev, K. M. Shiyapov

{"title":"有记忆的双曲型混合问题的隐式差分方案","authors":"Zh. A. Abdiramanov, Zh. D. Baishemirov, A. S. Berdyshev, K. M. Shiyapov","doi":"10.1134/s1995080224600249","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this article is proposed a method for numerically solving a mixed problem for a hyperbolic equation with memory. An implicit difference scheme is constructed as an effective means for solving complex multidimensional problems of mathematical physics. A condition is found for guaranteed stability of an implicit difference scheme for a mixed problem in the <span>\\(L^{2}\\)</span>-norm. The order of convergence for all variables of the presented difference scheme was calculated and confirmed by numerical experiment.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An Implicit Difference Scheme for a Mixed Problem of Hyperbolic Type with Memory\",\"authors\":\"Zh. A. Abdiramanov, Zh. D. Baishemirov, A. S. Berdyshev, K. M. Shiyapov\",\"doi\":\"10.1134/s1995080224600249\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>In this article is proposed a method for numerically solving a mixed problem for a hyperbolic equation with memory. An implicit difference scheme is constructed as an effective means for solving complex multidimensional problems of mathematical physics. A condition is found for guaranteed stability of an implicit difference scheme for a mixed problem in the <span>\\\\(L^{2}\\\\)</span>-norm. The order of convergence for all variables of the presented difference scheme was calculated and confirmed by numerical experiment.</p>\",\"PeriodicalId\":46135,\"journal\":{\"name\":\"Lobachevskii Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-05-14\",\"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/s1995080224600249\",\"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/s1995080224600249","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

摘要本文提出了一种数值求解有记忆双曲方程混合问题的方法。构建了一种隐式差分方案，作为求解复杂多维数学物理问题的有效手段。为保证混合问题的隐式差分方案在 \(L^{2}\) 规范下的稳定性，找到了一个条件。计算了所提出的差分方案的所有变量的收敛阶数，并通过数值实验予以证实。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

An Implicit Difference Scheme for a Mixed Problem of Hyperbolic Type with Memory

查看原文本刊更多论文

An Implicit Difference Scheme for a Mixed Problem of Hyperbolic Type with Memory

Abstract

In this article is proposed a method for numerically solving a mixed problem for a hyperbolic equation with memory. An implicit difference scheme is constructed as an effective means for solving complex multidimensional problems of mathematical physics. A condition is found for guaranteed stability of an implicit difference scheme for a mixed problem in the \(L^{2}\)-norm. The order of convergence for all variables of the presented difference scheme was calculated and confirmed by numerical experiment.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Lobachevskii Journal of Mathematics MATHEMATICS-

CiteScore

1.50

自引率

42.90%

发文量

127

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.