拉普拉斯变换在热方程中的应用

Ana Uzla BatuBara
{"title":"拉普拉斯变换在热方程中的应用","authors":"Ana Uzla BatuBara","doi":"10.55227/ijhet.v1i6.110","DOIUrl":null,"url":null,"abstract":"The one dimensional of homogeneous heat equation is two ordinary partial differential equations which general form , so needs solution. The one dimensional of homogeneous heat equation the method is ever been solved by Fourier series and Fourier Integrals. The other method used to in solving one dimensional of homogeneous heat equation is Laplace Transform, which is used to transform into ordinary differential equation is one dimension  for initial conditions . Inverse general solution that satisfies boundary conditions  is found, for every t and initial conditions  that have been transform is . From the result, it an obtain temperature on the poin x in the solid at time t.","PeriodicalId":426265,"journal":{"name":"International Journal of Health Engineering and Technology","volume":"10 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Application Of The Laplace Transform In The Heat Equation\",\"authors\":\"Ana Uzla BatuBara\",\"doi\":\"10.55227/ijhet.v1i6.110\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The one dimensional of homogeneous heat equation is two ordinary partial differential equations which general form , so needs solution. The one dimensional of homogeneous heat equation the method is ever been solved by Fourier series and Fourier Integrals. The other method used to in solving one dimensional of homogeneous heat equation is Laplace Transform, which is used to transform into ordinary differential equation is one dimension  for initial conditions . Inverse general solution that satisfies boundary conditions  is found, for every t and initial conditions  that have been transform is . From the result, it an obtain temperature on the poin x in the solid at time t.\",\"PeriodicalId\":426265,\"journal\":{\"name\":\"International Journal of Health Engineering and Technology\",\"volume\":\"10 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-03-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Health Engineering and Technology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.55227/ijhet.v1i6.110\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Health Engineering and Technology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.55227/ijhet.v1i6.110","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

一维齐次热方程是两个一般形式的常偏微分方程,因此需要求解。该方法对一维的齐次热方程采用傅里叶级数和傅里叶积分求解。另一种用于求解一维齐次热方程的方法是拉普拉斯变换,在初始条件下将其变换为一维常微分方程。求出满足边界条件的反通解,对于每一个t和已变换的初始条件为。由结果可以得到时间t时固体中x点的温度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Application Of The Laplace Transform In The Heat Equation
The one dimensional of homogeneous heat equation is two ordinary partial differential equations which general form , so needs solution. The one dimensional of homogeneous heat equation the method is ever been solved by Fourier series and Fourier Integrals. The other method used to in solving one dimensional of homogeneous heat equation is Laplace Transform, which is used to transform into ordinary differential equation is one dimension  for initial conditions . Inverse general solution that satisfies boundary conditions  is found, for every t and initial conditions  that have been transform is . From the result, it an obtain temperature on the poin x in the solid at time t.
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
0
×
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:604180095
Book学术官方微信