{"title":"二维电报方程的Crank-Nicolson搭配谱法。","authors":"Yanjie Zhou, Zhendong Luo","doi":"10.1186/s13660-018-1728-5","DOIUrl":null,"url":null,"abstract":"<p><p>In this paper, we mainly focus to study the Crank-Nicolson collocation spectral method for two-dimensional (2D) telegraph equations. For this purpose, we first establish a Crank-Nicolson collocation spectral model based on the Chebyshev polynomials for the 2D telegraph equations. We then discuss the existence, uniqueness, stability, and convergence of the Crank-Nicolson collocation spectral numerical solutions. Finally, we use two sets of numerical examples to verify the validity of theoretical analysis. This implies that the Crank-Nicolson collocation spectral model is very effective for solving the 2D telegraph equations.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"137"},"PeriodicalIF":1.6000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1728-5","citationCount":"9","resultStr":"{\"title\":\"A Crank-Nicolson collocation spectral method for the two-dimensional telegraph equations.\",\"authors\":\"Yanjie Zhou, Zhendong Luo\",\"doi\":\"10.1186/s13660-018-1728-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>In this paper, we mainly focus to study the Crank-Nicolson collocation spectral method for two-dimensional (2D) telegraph equations. For this purpose, we first establish a Crank-Nicolson collocation spectral model based on the Chebyshev polynomials for the 2D telegraph equations. We then discuss the existence, uniqueness, stability, and convergence of the Crank-Nicolson collocation spectral numerical solutions. Finally, we use two sets of numerical examples to verify the validity of theoretical analysis. This implies that the Crank-Nicolson collocation spectral model is very effective for solving the 2D telegraph equations.</p>\",\"PeriodicalId\":49163,\"journal\":{\"name\":\"Journal of Inequalities and Applications\",\"volume\":\"2018 1\",\"pages\":\"137\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1186/s13660-018-1728-5\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Inequalities and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1186/s13660-018-1728-5\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2018/6/19 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Inequalities and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s13660-018-1728-5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2018/6/19 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
A Crank-Nicolson collocation spectral method for the two-dimensional telegraph equations.
In this paper, we mainly focus to study the Crank-Nicolson collocation spectral method for two-dimensional (2D) telegraph equations. For this purpose, we first establish a Crank-Nicolson collocation spectral model based on the Chebyshev polynomials for the 2D telegraph equations. We then discuss the existence, uniqueness, stability, and convergence of the Crank-Nicolson collocation spectral numerical solutions. Finally, we use two sets of numerical examples to verify the validity of theoretical analysis. This implies that the Crank-Nicolson collocation spectral model is very effective for solving the 2D telegraph equations.
期刊介绍：
The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.
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