流动非线性及其同伦分析：流体力学和传热（英文版）

图书标准信息

• 作者 [美]瓦捷拉维鲁（Kuppalaplle Vajravelu）、[美]隔德（Robert A.Van Gorder） 著
• 出版社 高等教育出版社
• 出版时间 2012-08
• 版次 1
• ISBN 9787040354492
• 定价 69.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 190页
• 字数 280千字
• 正文语种 英语
• 丛书 非线性物理科学

【内容简介】

科学工程中的很多问题是非线性的，难以解决。传统的解析近似方法只对弱非线性问题有效，但无法很好地解决强非线性问题。同伦分析方法是近20年发展起来的一种有效的求解强非线性问题的解析近似方法。《流动非线性及其同伦分析：流体力学和传热（英文版）》介绍了同伦分析方法的最新理论进展，但不局限于方法的理论架构，也给出了大量的流体力学和传热中的非线性问题实例，来体现同伦分析方法的应用性。
《流动非线性及其同伦分析：流体力学和传热（英文版）》适合于物理、应用数学、非线性力学、金融和工程等领域对强非线性问题解析近似解感兴趣的科研人员和研究生。

【目录】

1Introduction
References
2PrinciplesofHomotopyAnalysis
2.1Principlesofhomotopyandthehomotopyanalysismethod.
2.2Constructionofthedeformationequations
2.3Constructionoftheseriessolution
2.4Conditionsfortheconvergenceoftheseriessolutions
2.5Existenceanduniquenessofsolutionsobtainedbyhomotopyanalysis
2.6Relationsbetweenthehomotopyanalysismethodandotheranalyticalmethods
2.7HomotopyanalysismethodfortheSwiftHohenbergequation
2.7.1Applicationofthehomotopyanalysismethod
2.7.2Convergenceoftheseriessolutionanddiscussionofresults
2.8Incompressibleviscousconductingfluidapproachingapermeablestretchingsurface
2.8.1Exactsolutionsforsomespecialcases
2.8.2ThecaseofG≠0
2.8.3ThecaseofG=0
2.8.4Numericalsolutionsanddiscussionoftheresults.
2.9Hydromagneticstagnationpointflowofasecondgradefluidoverastretchingsheet
2.9.1Formulationofthemathematicalproblem
2.9.2Exactsolutions
2.9.3Constructinganalyticalsolutionsviahomotopyanalysis
References

3MethodsfortheControlofConvergenceinObtainedSolutions
3.1Selectionoftheauxiliarylinearoperatorandbasefunctionrepresentation
3.1.1Methodoflinearpartitionmatching
3.1.2Methodofhighestorderdifferentialmatching
3.1.3Methodofcompletedifferentialmatching
3.1.4Initialversusboundaryvalueproblems
3.1.5Additionaloptionsfortheselectionofanauxiliarylinearoperator
3.1.6Remarksonthesolutionexpression
3.2Theroleoftheauxiliaryfunction
3.3Selectionoftheconvergencecontrolparameter
3.40ptimalconvergencecontrolparametervalueandtheLane-Emdenequationofthefirstkind
3.4.1Physicalbackground
3.4.2AnalyticsolutionsviaTaylorseries
3.4.3Analyticsolutionsviahomotopyanalysis
References

4AdditionalTechniques
4.1Constructionofmultiplehomotopiesforcoupledequations
4.2Selectionofanauxiliarynonlinearoperator
4.3Validationoftheconvergencecontrolparameter
4.3.1Convergencecontrolparameterplots（"h-plots"）
4.3.2Minimizedresidualerrors
4.3.3Minimizedapproximateresidualerrors
4.4MultiplehomotopiesandtheconstructionofsolutionstotheFoppl-vonKarmanequationsgoverningdefiectionsofathinflatplate
4.4.1Physicalbackground
4.4.2Linearizationandconstructionofperturbationsolutions
4.4.3Recursivesolutionsfortheclampededgeboundarydata
4.4.4Specialcase:Thethinplatelimith→0,v2→1
4.4.5Controloferrorandselectionoftheconvergencecontrolparameters
4.5NonlinearauxiliaryoperatorsandlocalsolutionstotheDrinfel'd-Sokolovequations
4.6RecentworkonadvancedtechniquesinHAM
4.6.1Mathematicalpropertiesofh-curveintheframeworkofthehomotopyanalysismethod
4.6.2Predictorhomotopyanalysismethodanditsapplicationtosomenonlinearproblems
4.6.3Anoptimalhomotopy-analysisapproachforstronglynonlineardifferentialequations
4.6.4Onthehomotopymultiple-variablemethodanditsapplicationsintheinteractionsofnonlineargravity
References

5ApplicationoftheHomotopyAnalysisMethodtoFluidFlowProblems
6FurtherApplicationsoftheHomotopyAnalysisMethod
SubjectIndex
AuthorIndex