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

IF 2.4 Q2 ENGINEERING, MECHANICAL Nonlinear Engineering - Modeling and Application Pub Date : 2023-01-01 DOI:10.1515/nleng-2022-0280
Mamta Kapoor
{"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}
引用次数: 0

摘要

摘要本文对比了一维和二维双曲电报方程的两种数值形式。第一种实现形式为均匀代数三角张力b样条DQM,第二种实现形式为均匀代数双曲张力b样条DQM。将上述方程进行空间离散化后,用SSP RK43方法求解得到的ode系统。为了评估所选战术的成功,给出了错误的比较。图中可以看到,并断言,精度和数值结果是一致的。并给出了收敛性和稳定性分析。应该强调的是,目前缺乏对一维和二维双曲电报方程的研究。这项研究的目的是有效地创造更少错误的结果。这些技术对于其他高阶非线性复杂性质的偏微分方程,包括分数阶方程、积分方程和部分积分方程,肯定是有用的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
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.
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
CiteScore
6.20
自引率
3.60%
发文量
49
审稿时长
44 weeks
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.
期刊最新文献
Study of time-fractional delayed differential equations via new integral transform-based variation iteration technique Convolutional neural network for UAV image processing and navigation in tree plantations based on deep learning Nonlinear adaptive sliding mode control with application to quadcopters Equilibrium stability of dynamic duopoly Cournot game under heterogeneous strategies, asymmetric information, and one-way R&D spillovers A versatile dynamic noise control framework based on computer simulation and modeling
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1