改进Boussinesq方程的k = 1有限元数值解

Fidel Contreras López, Eusebio Tapia, F. Ongay, M. Agüero
{"title":"改进Boussinesq方程的k = 1有限元数值解","authors":"Fidel Contreras López, Eusebio Tapia, F. Ongay, M. Agüero","doi":"10.4236/IJMNTA.2015.41006","DOIUrl":null,"url":null,"abstract":"The improved Boussinesq equation is solved with classical finite element method using the most basic Lagrange element k = 1, which leads us to a second order nonlinear ordinary differential equations system in time; this can be solved by any standard accurate numerical method for example Runge-Kutta-Fehlberg. The technique is validated with a typical example and a fourth order convergence in space is confirmed; the 1- and 2-soliton solutions are used to simulate wave travel, wave splitting and interaction; solution blow up is described graphically. The computer symbolic system MathLab is quite used for numerical simulation in this paper; the known results in the bibliography are confirmed.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":"04 1","pages":"88-99"},"PeriodicalIF":0.0000,"publicationDate":"2015-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"The k = 1 Finite Element Numerical Solution for the Improved Boussinesq Equation\",\"authors\":\"Fidel Contreras López, Eusebio Tapia, F. Ongay, M. Agüero\",\"doi\":\"10.4236/IJMNTA.2015.41006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The improved Boussinesq equation is solved with classical finite element method using the most basic Lagrange element k = 1, which leads us to a second order nonlinear ordinary differential equations system in time; this can be solved by any standard accurate numerical method for example Runge-Kutta-Fehlberg. The technique is validated with a typical example and a fourth order convergence in space is confirmed; the 1- and 2-soliton solutions are used to simulate wave travel, wave splitting and interaction; solution blow up is described graphically. The computer symbolic system MathLab is quite used for numerical simulation in this paper; the known results in the bibliography are confirmed.\",\"PeriodicalId\":69680,\"journal\":{\"name\":\"现代非线性理论与应用(英文)\",\"volume\":\"04 1\",\"pages\":\"88-99\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-02-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"现代非线性理论与应用(英文)\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://doi.org/10.4236/IJMNTA.2015.41006\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"现代非线性理论与应用(英文)","FirstCategoryId":"1093","ListUrlMain":"https://doi.org/10.4236/IJMNTA.2015.41006","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2

摘要

利用最基本的拉格朗日元k = 1,用经典有限元法求解改进的Boussinesq方程,得到一个二阶非线性常微分方程组;这可以用任何标准的精确数值方法求解,例如龙格-库塔-费贝格法。通过一个典型实例验证了该方法的有效性,并证实了该方法在空间上具有四阶收敛性;用1孤子解和2孤子解模拟波的传播、波的分裂和相互作用;溶液爆破用图形描述。本文主要使用计算机符号系统MathLab进行数值模拟;参考书目中已知的结果得到了确认。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The k = 1 Finite Element Numerical Solution for the Improved Boussinesq Equation
The improved Boussinesq equation is solved with classical finite element method using the most basic Lagrange element k = 1, which leads us to a second order nonlinear ordinary differential equations system in time; this can be solved by any standard accurate numerical method for example Runge-Kutta-Fehlberg. The technique is validated with a typical example and a fourth order convergence in space is confirmed; the 1- and 2-soliton solutions are used to simulate wave travel, wave splitting and interaction; solution blow up is described graphically. The computer symbolic system MathLab is quite used for numerical simulation in this paper; the known results in the bibliography are confirmed.
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
111
×
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