{"title":"用UAT和UAH张力b样条DQM进行一维和二维双曲电报方程数值逼近的比较研究","authors":"Mamta Kapoor","doi":"10.1515/nleng-2022-0280","DOIUrl":null,"url":null,"abstract":"Abstract Two numerical regimes for the one- and two-dimensional hyperbolic telegraph equations are contrasted in this article. The first implemented regime is uniform algebraic trigonometric tension B-spline DQM, while the second implemented regime is uniform algebraic hyperbolic tension B-spline DQM. The resulting system of ODEs is solved by the SSP RK43 method after the aforementioned equations are spatially discretized. To assess the success of chosen tactics, a comparison of errors is shown. The graphs can be seen, and it is asserted that the precise and numerical results are in agreement with one another. Analyses of convergence and stability are also given. It should be highlighted that there is a dearth of study on 1D and 2D hyperbolic telegraph equations. This aim of this study is to efficiently create results with fewer mistakes. These techniques would surely be useful for other higher-order nonlinear complex natured partial differential equations, including fractional equations, integro equations, and partial-integro equations.","PeriodicalId":37863,"journal":{"name":"Nonlinear Engineering - Modeling and Application","volume":"98 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A comparative study for the numerical approximation of 1D and 2D hyperbolic telegraph equations with UAT and UAH tension B-spline DQM\",\"authors\":\"Mamta Kapoor\",\"doi\":\"10.1515/nleng-2022-0280\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Two numerical regimes for the one- and two-dimensional hyperbolic telegraph equations are contrasted in this article. The first implemented regime is uniform algebraic trigonometric tension B-spline DQM, while the second implemented regime is uniform algebraic hyperbolic tension B-spline DQM. The resulting system of ODEs is solved by the SSP RK43 method after the aforementioned equations are spatially discretized. To assess the success of chosen tactics, a comparison of errors is shown. The graphs can be seen, and it is asserted that the precise and numerical results are in agreement with one another. Analyses of convergence and stability are also given. It should be highlighted that there is a dearth of study on 1D and 2D hyperbolic telegraph equations. This aim of this study is to efficiently create results with fewer mistakes. These techniques would surely be useful for other higher-order nonlinear complex natured partial differential equations, including fractional equations, integro equations, and partial-integro equations.\",\"PeriodicalId\":37863,\"journal\":{\"name\":\"Nonlinear Engineering - Modeling and Application\",\"volume\":\"98 1\",\"pages\":\"\"},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Engineering - Modeling and Application\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/nleng-2022-0280\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Engineering - Modeling and Application","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/nleng-2022-0280","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
A comparative study for the numerical approximation of 1D and 2D hyperbolic telegraph equations with UAT and UAH tension B-spline DQM
Abstract Two numerical regimes for the one- and two-dimensional hyperbolic telegraph equations are contrasted in this article. The first implemented regime is uniform algebraic trigonometric tension B-spline DQM, while the second implemented regime is uniform algebraic hyperbolic tension B-spline DQM. The resulting system of ODEs is solved by the SSP RK43 method after the aforementioned equations are spatially discretized. To assess the success of chosen tactics, a comparison of errors is shown. The graphs can be seen, and it is asserted that the precise and numerical results are in agreement with one another. Analyses of convergence and stability are also given. It should be highlighted that there is a dearth of study on 1D and 2D hyperbolic telegraph equations. This aim of this study is to efficiently create results with fewer mistakes. These techniques would surely be useful for other higher-order nonlinear complex natured partial differential equations, including fractional equations, integro equations, and partial-integro equations.
期刊介绍:
The Journal of Nonlinear Engineering aims to be a platform for sharing original research results in theoretical, experimental, practical, and applied nonlinear phenomena within engineering. It serves as a forum to exchange ideas and applications of nonlinear problems across various engineering disciplines. Articles are considered for publication if they explore nonlinearities in engineering systems, offering realistic mathematical modeling, utilizing nonlinearity for new designs, stabilizing systems, understanding system behavior through nonlinearity, optimizing systems based on nonlinear interactions, and developing algorithms to harness and leverage nonlinear elements.