椭圆型微分方程
2006-1
科学出版社
哈克布施
311
381000
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本书论述了椭圆型微分方程的理论与数值处理。主要内容包括古典理论(格林函数、极大值原理等)和变分公式化。作者阐述并分析了有限差分方法和有限元方法。某些章节特别讨论了特征值问题和斯托克斯问题。
作者：(德)哈克布施
ForewordTable of ContentsNotation1 PartialDifferentialEquationsandTheirClassificationIntoTypes 1.1 Examples 1.2 ClassificationofSecond-OrderEquationsintoTypes 1.3 TypeClassificationforSystemsofFirstOrder 1.4 CharacteristicPropertiesoftheDifferentTypes2 ThePotentialEquation 2.1 PosingtheProblem 2.2 SingularityFunction 2.3 TheMeanValuePropertyandMaximumPrinciple 2.4 ContinuousDependenceontheBoundaryData3 ThePoissonEquation 3.1 PosingtheProblem 3.2 RepressentationoftheSolutionbytheGreenFunction 3.3 TheGreenFunctionfortheBall 3.4 TheNeumannBoundaryValueProblem 3.5 TheIntegralEquationMethod4 DifferenceMethodsforthePoissonEquation 4.1 Introduction:TheOne-DimensionalCase 4.2 TheFive-PointFormula 4.3 M-matrices,MatrixNorms,PositiveDefiniteMatrices 4.4 PropertiesoftheMartrixLh 4.5 Convergence 4.6 DiscretisationsofHigherOrder 4.7 TheDiscretisationoftheNeumann 4.8 DiscretisationinandArbitraryDomain5 GeneralBoundaryValueProblems 5.1 DirichletBoundaryValueProblemsforLinear 5.2 GeneralBoundaryConditions 5.3 BoundaryProblemsofHigherOrder6 ToolsfromFunctionalAnalysis 6.1 BanachSpacesandHilbertSpaces 6.2 SobolevSpaces 6.3 DualSpaces 6.4 CompactOperators 6.5 BilinearForms7 VariationalFormulation 7.1 HistoricalRemarks 7.2 EquationswithHomogeneousDirichletboundaryConditions 7.3 InhomogeneousDirichletboundaryConditions 7.4 NaturalBoundaryConditions8 TheMethodofFiniteElements 8.1 TheRitz-GalerkinMethod 8.2 ErrorEstimates 8.3 FiniteElements 8.4 ErrorEstimatesforFiniteElementMethods 8.5 Generalisations 8.6 FiniteElementsforNon-PoluygonalRegions 8.7 AdditionalRemarks 8.8 PropertiesoftheStiffnessMatrix9 Regularity 9.1 SolutionsoftheBoundaryValueProblem 9.2 RegularityPropertiesofDifferenceEquations10 SpecialDifferentialEquations 10.1 DifferentialEquationswithDiscontinuousCoefficients 10.2 ASingularPerturbationProblem11 EigenvalueProblems 11.1 FormulationofEigenvalueProblems 11.2 FiniteElementDiscretisation 11.3 DiscretisationbyDifferenceMethods12 Stokesequations 12.1 SystmesofEllipticDifferentialEquations 12.2 Variationalformulation 12.3 MixedFinite-ElementMethodfortheStokesProblemBiblographyIndex
《椭圆型微分方程:理论与数值处理》是科学出版社出版。
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字迹清楚，纸张上乘，内容不错
写的很好，对我本人很有益！