{"title":"Exact Solution to Bratu Second Order Differential Equation","authors":"Adam R. Szewczyk","doi":"10.1016/S0034-4877(24)00075-2","DOIUrl":null,"url":null,"abstract":"<div><div>This paper deals with the temperature profile of a simple combustion and presents the alternative exact formulas for the temperature profile of the planar vessel. The differential equation that describes this system is referred as a Bratu equation or Poisson's equation in one-dimensional steady state case. In this present study, new solutions with general boundary conditions are developed. The results are compared with numerical solutions using Maxima, a computer algebra system program capable of numerical and symbolic computation. The new solutions yield formula that may provide a valuable information about relationship between terms, variables and coefficients which can be useful for theoretical physics.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 2","pages":"Pages 175-188"},"PeriodicalIF":1.0000,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0034487724000752","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
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Abstract
This paper deals with the temperature profile of a simple combustion and presents the alternative exact formulas for the temperature profile of the planar vessel. The differential equation that describes this system is referred as a Bratu equation or Poisson's equation in one-dimensional steady state case. In this present study, new solutions with general boundary conditions are developed. The results are compared with numerical solutions using Maxima, a computer algebra system program capable of numerical and symbolic computation. The new solutions yield formula that may provide a valuable information about relationship between terms, variables and coefficients which can be useful for theoretical physics.
期刊介绍：
Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.
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