求解三阶色散偏微分方程的四次非多项式样条

Z. M. Alaofi, Talaat Sayed Ali, F. A. Alaal, S. Dragomir
{"title":"求解三阶色散偏微分方程的四次非多项式样条","authors":"Z. M. Alaofi, Talaat Sayed Ali, F. A. Alaal, S. Dragomir","doi":"10.4236/ajcm.2021.113013","DOIUrl":null,"url":null,"abstract":"In the present paper, we introduce a non-polynomial quadratic spline method for solving third-order boundary value problems. Third-order singularly perturbed boundary value problems occur frequently in many areas of applied sciences such as solid mechanics, quantum mechanics, chemical reactor theory, Newtonian fluid mechanics, optimal control, convection-diffusion proc-esses, hydrodynamics, aerodynamics, etc. These problems have various im-portant applications in fluid dynamics. The procedure involves a reduction of a third-order partial differential equation to a first-order ordinary differential equation. Truncation errors are given. The unconditional stability of the method is analysed by the Von-Neumann stability analysis. The developed method is tested with an illustrated example, and the results are compared with other methods from the literature, which shows the applicability and feasibility of the presented method. Furthermore, a graphical comparison between analytical and approximate solutions is also shown for the illustrated example.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Quartic Non-Polynomial Spline for Solving the Third-Order Dispersive Partial Differential Equation\",\"authors\":\"Z. M. Alaofi, Talaat Sayed Ali, F. A. Alaal, S. Dragomir\",\"doi\":\"10.4236/ajcm.2021.113013\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the present paper, we introduce a non-polynomial quadratic spline method for solving third-order boundary value problems. Third-order singularly perturbed boundary value problems occur frequently in many areas of applied sciences such as solid mechanics, quantum mechanics, chemical reactor theory, Newtonian fluid mechanics, optimal control, convection-diffusion proc-esses, hydrodynamics, aerodynamics, etc. These problems have various im-portant applications in fluid dynamics. The procedure involves a reduction of a third-order partial differential equation to a first-order ordinary differential equation. Truncation errors are given. The unconditional stability of the method is analysed by the Von-Neumann stability analysis. The developed method is tested with an illustrated example, and the results are compared with other methods from the literature, which shows the applicability and feasibility of the presented method. Furthermore, a graphical comparison between analytical and approximate solutions is also shown for the illustrated example.\",\"PeriodicalId\":64456,\"journal\":{\"name\":\"美国计算数学期刊(英文)\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"美国计算数学期刊(英文)\",\"FirstCategoryId\":\"1089\",\"ListUrlMain\":\"https://doi.org/10.4236/ajcm.2021.113013\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"美国计算数学期刊(英文)","FirstCategoryId":"1089","ListUrlMain":"https://doi.org/10.4236/ajcm.2021.113013","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1

摘要

本文引入一种求解三阶边值问题的非多项式二次样条法。三阶奇摄动边值问题经常出现在固体力学、量子力学、化学反应器理论、牛顿流体力学、最优控制、对流扩散过程、流体力学、空气动力学等应用科学的许多领域。这些问题在流体动力学中有各种重要的应用。这个过程包括把一个三阶偏微分方程化为一个一阶常微分方程。给出了截断误差。用Von-Neumann稳定性分析方法分析了该方法的无条件稳定性。通过算例对所提出的方法进行了验证,并与文献中其他方法进行了比较,表明了所提出方法的适用性和可行性。此外,还给出了解析解和近似解的图解比较。
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
Quartic Non-Polynomial Spline for Solving the Third-Order Dispersive Partial Differential Equation
In the present paper, we introduce a non-polynomial quadratic spline method for solving third-order boundary value problems. Third-order singularly perturbed boundary value problems occur frequently in many areas of applied sciences such as solid mechanics, quantum mechanics, chemical reactor theory, Newtonian fluid mechanics, optimal control, convection-diffusion proc-esses, hydrodynamics, aerodynamics, etc. These problems have various im-portant applications in fluid dynamics. The procedure involves a reduction of a third-order partial differential equation to a first-order ordinary differential equation. Truncation errors are given. The unconditional stability of the method is analysed by the Von-Neumann stability analysis. The developed method is tested with an illustrated example, and the results are compared with other methods from the literature, which shows the applicability and feasibility of the presented method. Furthermore, a graphical comparison between analytical and approximate solutions is also shown for the illustrated example.
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
自引率
0.00%
发文量
348
期刊最新文献
Diophantine Quotients and Remainders with Applications to Fermat and Pythagorean Equations Quantization of the Kinetic Energy of Deterministic Chaos On Fermat Last Theorem: The New Efficient Expression of a Hypothetical Solution as a Function of Its Fermat Divisors Analyzing Electric Circuits with Computer Algebra Arithmetic Operations of Generalized Trapezoidal Picture Fuzzy Numbers by Vertex Method
×
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