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丛书简介
力学基础与工程技术前沿
同伦分析方法与非线性微分方程(英文版)
作 者:
廖世俊
ISBN:978-7-04-032298-9 出版时间:2012-02-09
全书目录
本章目录
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目录
FrontMatter
PartIBasicIdeasandTheorems
1Introduction
2BasicIdeasoftheHomotopyAnalysisMethod
3OptimalHomotopyAnalysisMethod
4SystematicDescriptionsandRelatedTheorems
5RelationshiptoEulerTransform
6SomeMethodsBasedontheHAM
PartIIMathematicaPackageBVPhandItsApplications
7MathematicaPackageBVPh
8NonlinearBoundary-valueProblemswithMultipleSolutions
9NonlinearEigenvalueEquationswithVaryingCoefficients
10ABoundary-layerFlowwithanInfiniteNumberofSolutions
11Non-similarityBoundary-layerFlows
12UnsteadyBoundary-layerFlows
PartIIIApplicationsinNonlinearPartialDifferentialEquations
13ApplicationsinFinance:AmericanPutOptions
14TwoandThreeDimensionalGelfandEquation
15InteractionofNonlinearWaterWaveandNonuniformCurrents
16ResonanceofArbitraryNumberofPeriodicTravelingWaterWaves
Index
4.1Briefframeofthehomotopyanalysismethod
4.2Propertiesofhomotopy-derivative
4.3Deformationequations
4.3.1Abriefhistory
4.3.2High-orderdeformationequations
4.3.3Examples
4.4Convergencetheorems
4.5Solutionexpression
4.5.1Choiceofinitialapproximation
4.5.2Choiceofauxiliarylinearoperator
4.6Convergencecontrolandacceleration
4.6.1Optimalconvergence-controlparameter
4.6.2Optimalinitialapproximation
4.6.3Homotopy-iterationtechnique
4.6.4Homotopy-Pad′etechnique
4.7Discussionsandopenquestions
References
4SystematicDescriptionsandRelatedTheorems
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