带罗宾边界条件的奇异扰动对流扩散方程耦合系统的高精度方法

IF 1.4 4区 物理与天体物理 Q2 MATHEMATICS, APPLIED
H. M. Ahmed
{"title":"带罗宾边界条件的奇异扰动对流扩散方程耦合系统的高精度方法","authors":"H. M. Ahmed","doi":"10.1007/s44198-024-00182-4","DOIUrl":null,"url":null,"abstract":"<p>This paper’s major goal is to provide a numerical approach for estimating solutions to a coupled system of convection–diffusion equations with Robin boundary conditions (RBCs). We devised a novel method that used four homogeneous RBCs to generate basis functions using generalized shifted Legendre polynomials (GSLPs) that satisfy these RBCs. We provide new operational matrices for the derivatives of the developed polynomials. The collocation approach and these operational matrices are utilized to find approximate solutions for the system under consideration. The given system subject to RBCs is turned into a set of algebraic equations that can be solved using any suitable numerical approach utilizing this technique. Theoretical convergence and error estimates are investigated. In conclusion, we provide three illustrative examples to demonstrate the practical implementation of the theoretical study we have just presented, highlighting the validity, usefulness, and applicability of the developed approach. The computed numerical results are compared to those obtained by other approaches. The methodology used in this study demonstrates a high level of concordance between approximate and exact solutions, as shown in the presented tables and figures.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Highly Accurate Method for a Singularly Perturbed Coupled System of Convection–Diffusion Equations with Robin Boundary Conditions\",\"authors\":\"H. M. Ahmed\",\"doi\":\"10.1007/s44198-024-00182-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This paper’s major goal is to provide a numerical approach for estimating solutions to a coupled system of convection–diffusion equations with Robin boundary conditions (RBCs). We devised a novel method that used four homogeneous RBCs to generate basis functions using generalized shifted Legendre polynomials (GSLPs) that satisfy these RBCs. We provide new operational matrices for the derivatives of the developed polynomials. The collocation approach and these operational matrices are utilized to find approximate solutions for the system under consideration. The given system subject to RBCs is turned into a set of algebraic equations that can be solved using any suitable numerical approach utilizing this technique. Theoretical convergence and error estimates are investigated. In conclusion, we provide three illustrative examples to demonstrate the practical implementation of the theoretical study we have just presented, highlighting the validity, usefulness, and applicability of the developed approach. The computed numerical results are compared to those obtained by other approaches. The methodology used in this study demonstrates a high level of concordance between approximate and exact solutions, as shown in the presented tables and figures.</p>\",\"PeriodicalId\":48904,\"journal\":{\"name\":\"Journal of Nonlinear Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-03-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Nonlinear Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1007/s44198-024-00182-4\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Nonlinear Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s44198-024-00182-4","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0

摘要

本文的主要目标是提供一种数值方法,用于估算具有罗宾边界条件(RBC)的对流-扩散耦合方程组的解。我们设计了一种新方法,利用四个均质 RBC,使用满足这些 RBC 的广义移位 Legendre 多项式 (GSLP) 生成基函数。我们为所开发多项式的导数提供了新的运算矩阵。我们利用配位法和这些运算矩阵为所考虑的系统找到近似解。受 RBCs 影响的给定系统被转化为一组代数方程,可以使用任何合适的数值方法利用该技术求解。我们对理论收敛性和误差估计进行了研究。最后,我们提供了三个示例来演示我们刚刚介绍的理论研究的实际应用,突出了所开发方法的有效性、实用性和适用性。计算出的数值结果与其他方法得出的结果进行了比较。本研究中使用的方法在近似解和精确解之间表现出高度的一致性,如所展示的表格和数字所示。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Highly Accurate Method for a Singularly Perturbed Coupled System of Convection–Diffusion Equations with Robin Boundary Conditions

Highly Accurate Method for a Singularly Perturbed Coupled System of Convection–Diffusion Equations with Robin Boundary Conditions

This paper’s major goal is to provide a numerical approach for estimating solutions to a coupled system of convection–diffusion equations with Robin boundary conditions (RBCs). We devised a novel method that used four homogeneous RBCs to generate basis functions using generalized shifted Legendre polynomials (GSLPs) that satisfy these RBCs. We provide new operational matrices for the derivatives of the developed polynomials. The collocation approach and these operational matrices are utilized to find approximate solutions for the system under consideration. The given system subject to RBCs is turned into a set of algebraic equations that can be solved using any suitable numerical approach utilizing this technique. Theoretical convergence and error estimates are investigated. In conclusion, we provide three illustrative examples to demonstrate the practical implementation of the theoretical study we have just presented, highlighting the validity, usefulness, and applicability of the developed approach. The computed numerical results are compared to those obtained by other approaches. The methodology used in this study demonstrates a high level of concordance between approximate and exact solutions, as shown in the presented tables and figures.

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
Journal of Nonlinear Mathematical Physics
Journal of Nonlinear Mathematical Physics PHYSICS, MATHEMATICAL-PHYSICS, MATHEMATICAL
CiteScore
1.60
自引率
0.00%
发文量
67
审稿时长
3 months
期刊介绍: Journal of Nonlinear Mathematical Physics (JNMP) publishes research papers on fundamental mathematical and computational methods in mathematical physics in the form of Letters, Articles, and Review Articles. Journal of Nonlinear Mathematical Physics is a mathematical journal devoted to the publication of research papers concerned with the description, solution, and applications of nonlinear problems in physics and mathematics. The main subjects are: -Nonlinear Equations of Mathematical Physics- Quantum Algebras and Integrability- Discrete Integrable Systems and Discrete Geometry- Applications of Lie Group Theory and Lie Algebras- Non-Commutative Geometry- Super Geometry and Super Integrable System- Integrability and Nonintegrability, Painleve Analysis- Inverse Scattering Method- Geometry of Soliton Equations and Applications of Twistor Theory- Classical and Quantum Many Body Problems- Deformation and Geometric Quantization- Instanton, Monopoles and Gauge Theory- Differential Geometry and Mathematical Physics
×
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
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
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 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信