橢圓型微分方程

內(nèi)容概要

本書(shū)論述了橢圓型微分方程的理論與數(shù)值處理。主要內(nèi)容包括古典理論(格林函數(shù)、極大值原理等)和變分公式化。作者闡述并分析了有限差分方法和有限元方法。某些章節(jié)特別討論了特征值問(wèn)題和斯托克斯問(wèn)題。

作者簡(jiǎn)介

作者：(德)哈克布施

書(shū)籍目錄

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

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