偏微分方程的数值方法：英文版

SeriesPreface.
Preface
PrefacetoPart1
ContentsofPart1
StabilityofInitial-Boundary-ValueSchemes
8.1Introduction
8.2Stability
8.2.1Stability:AnEasyCase
8.2.2Stability:AnotherEasyCase
8.2.3GKSO:GeneralTheory
8.2.4LeftQuarterPlaneProblems
8.3ConstructingStableDifferenceSchemes
8.4ConsistencyandConvergence
8.4.1NormsandConsistency
8.4.2ConsistencyofNumericalBoundaryConditions
8.4.3ConvergenceTheorem:Gustafsson
8.5SchemesWithoutNumericalBoundaryConditions
8.6ParabolicInitial-Boundary-ValueProblems
9ConservationLaws
9.1Introduction
9.2TheoryofScalarConservationLaws
9.2.1ShockFormation
9.2.2WeakSolutions
9.2.3DiscontinuousSolutions
9.2.4TheEntropyCondition
9.2.5SolutionofScalarConservationLaws
9.3TheoryofSystemsofConservationLaws
9.3.1SolutionsofPdemannProblems
9.4ComputationalInterludeVI
9.5NumericalSolutionofConservationLaws
9.5.1Introduction
9.6DifferenceSchemesforConservationLaws
9.6.1Consistency
9.6.2ConservativeSchemes
9.6.3DiscreteConservation
9.6.4TheCourant-Friedrichs-LewyCondition
9.6.5Entropy
9.7DifferenceSchemesforScalarConservationLaws
9.7.1Definitions
9.7.2Theorems
9.7.3GodunovScheme
9.7.4HighResolutionSchemes
9.7.5Flux-LimiterMethods
9.7.6Slope-LimiterMethods
9.7.7ModifiedFluxMethod
9.8DifferenceSchemesforK-SystemConservationLaws
9.9GodunovSchemes
9.9.1GodunovSchemesforLinearK-System
ConservationLaws
9.9.2GodunovSchemesforK-SystemConservationLaws
9.9.3ApproximateRiemannSolvers:Theory
9.9.4ApproximateRiemannSolvers:Applications
9.10HighResolutionSchemesforLinearK-System
ConservationLaws
9.10.1Flux-LimiterSchemesforLinearK-System
ConservationLaws
9.10.2Slope-LimiterSchemesforLinearK-System
ConservationLaws
9.10.3AModifiedFluxSchemeforLinearK-System
ConservationLaws
9.10.4HighResolutionSchemesforK-System
ConservationLaws
9.11ImplicitSchemes
9.12DifferenceSchemesforTwoDimensionalConservationLaws..
9.12.1SomeComputationalExamples
9.12.2SomeTwoDimensionalHighResolutionSchemes
9.12.3TheZalesak-SmolarkiewiczScheme
9.12.4AZ-SSchemeforNonlinearConservationLaws
9.12.5TwoDimensionalK-SystemConservationLaws
10EllipticEquations
10.1Introduction
10.2SolvabilityofEllipticDifferenceEquations:Dirichlet
BoundaryConditions
10.3ConvergenceofEllipticDifferenceSchemes:Dirichlet
BoundaryConditions
10.4SolutionSchemesforEllipticDifferenceEquations:
Introduction
10.5ResidualCorrectionMethods
10.5.1AnalysisofResidualCorrectionSchemes
10.5.2JacobiRelaxationScheme
10.5.3AnalysisoftheJacobiRelaxationScheme
10.5.4StoppingCriteria
10.5.5ImplementationoftheJacobiScheme
10.5.6Gauss-SeidelScheme
10.5.7AnalysisoftheGauss-SeidelRelaxationScheme
10.5.8SuccessiveOverrelaxationScheme
10.5.9ElementaryAnalysisofSORScheme
10.5.10MoreontheSORScheme
10.5.11LineJacobi,Gauss-SeidelandSORSchemes
10.5.12Approximatingwb:Reality
10.6EllipticDifferenceEquations:Neumann
BoundaryConditions
10.6.1FirstOrderApproximation
10.6.2SecondOrderApproximation
10.6.3SecondOrderApproximationonanOffsetGrid
10.7NumericalSolutionofNeumannProblems
10.7.1Introduction
10.7.2ResidualCorrectionSchemes
10.7.3JacobiandGauss-SeidelIteration
10.7.4SORScheme
10.7.5Approximationofwb
10.7.6Implementation:NeumannProblems
10.8EllipticDifferenceEquations:MixedProblems
10.8.1Introduction
10.8.2MixedProblems:Solvability
10.8.3MixedProblems:Implementation
10.9EllipticDifferenceEquations:PolarCoordinates
10.10Multigrid
10.10.1Introduction
10.10.2Smoothers
10.10.3GridTransfers
10.10.4MultigridAlgorithm
10.11ComputationalInterludeVII
10.11.1BlockingOut:IrregularRegions
10.11.2HW0.0.4
10.12ADISchemes
10.13ConjugateGradientScheme
10.13.1PreconditionedConjugateGradientScheme
10.13.2SSORasaPreconditioner
10.13.3Implementation
10.14UsingIterativeMethodstoSolveTimeDependentProblems
10.15UsingFFTstoSolveEllipticProblems
10.16ComputationalInterludeVIII
11IrregularRegionsandGrids
11.1Introduction
11.2IrregularGeometries
11.2.1BlockingOut
11.2.9.MaptheRegion
11.2.3GridGeneration
11.3GridRefinement
11.3.1GridRefinement:ExplicitSchemesforHyperbolic
Problems
11.3.2GridRefinementforImplicitSchemes
11.4UnstructuredGrids
References
Index...