艾伦-卡恩方程的近似分析和数值解法比较

IF 1.4 Q2 MATHEMATICS, APPLIED
S. Hussain, Fazal Haq, Abdullah Shah, D. Abduvalieva, Ali Shokri
{"title":"艾伦-卡恩方程的近似分析和数值解法比较","authors":"S. Hussain, Fazal Haq, Abdullah Shah, D. Abduvalieva, Ali Shokri","doi":"10.1155/2024/8835138","DOIUrl":null,"url":null,"abstract":"Allen Cahn (AC) equation is highly nonlinear due to the presence of cubic term and also very stiff; therefore, it is not easy to find its exact analytical solution in the closed form. In the present work, an approximate analytical solution of the AC equation has been investigated. Here, we used the variational iteration method (VIM) to find approximate analytical solution for AC equation. The obtained results are compared with the hyperbolic function solution and traveling wave solution. Results are also compared with the numerical solution obtained by using the finite difference method (FDM). Absolute error analysis tables are used to validate the series solution. A convergent series solution obtained by VIM is found to be in a good agreement with the analytical and numerical solutions.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Comparison of Approximate Analytical and Numerical Solutions of the Allen Cahn Equation\",\"authors\":\"S. Hussain, Fazal Haq, Abdullah Shah, D. Abduvalieva, Ali Shokri\",\"doi\":\"10.1155/2024/8835138\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Allen Cahn (AC) equation is highly nonlinear due to the presence of cubic term and also very stiff; therefore, it is not easy to find its exact analytical solution in the closed form. In the present work, an approximate analytical solution of the AC equation has been investigated. Here, we used the variational iteration method (VIM) to find approximate analytical solution for AC equation. The obtained results are compared with the hyperbolic function solution and traveling wave solution. Results are also compared with the numerical solution obtained by using the finite difference method (FDM). Absolute error analysis tables are used to validate the series solution. A convergent series solution obtained by VIM is found to be in a good agreement with the analytical and numerical solutions.\",\"PeriodicalId\":55967,\"journal\":{\"name\":\"International Journal of Differential Equations\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-03-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Differential Equations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2024/8835138\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2024/8835138","RegionNum":0,"RegionCategory":null,"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

由于存在立方项,艾伦-卡恩(AC)方程是一个高度非线性的方程,而且非常僵硬;因此,要找到其闭合形式的精确解析解并不容易。在本研究中,我们研究了 AC 方程的近似解析解。在这里,我们使用变分迭代法(VIM)来寻找交流方程的近似解析解。所得结果与双曲函数解法和行波解法进行了比较。我们还将所得结果与使用有限差分法(FDM)获得的数值解进行了比较。绝对误差分析表用于验证序列解。发现 VIM 获得的收敛级数解与分析解和数值解非常一致。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Comparison of Approximate Analytical and Numerical Solutions of the Allen Cahn Equation
Allen Cahn (AC) equation is highly nonlinear due to the presence of cubic term and also very stiff; therefore, it is not easy to find its exact analytical solution in the closed form. In the present work, an approximate analytical solution of the AC equation has been investigated. Here, we used the variational iteration method (VIM) to find approximate analytical solution for AC equation. The obtained results are compared with the hyperbolic function solution and traveling wave solution. Results are also compared with the numerical solution obtained by using the finite difference method (FDM). Absolute error analysis tables are used to validate the series solution. A convergent series solution obtained by VIM is found to be in a good agreement with the analytical and numerical solutions.
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
3.10
自引率
0.00%
发文量
20
审稿时长
20 weeks
×
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