偏微分方程的数值方法

　　Mathematics is playing an ever more important role in the physical and biological sciences， provoking a blurring of boundaries between scientific disciplines and a resurgence of interest'in the modern as well as the classical techniques of applied mathematics. This renewal of interest， both in research and teaching， has led to the establishment of the series： Texts in AppliedMathe- rustics （TAM）. The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques， such as numerical and symbolic computer systems， dynamical systems， and chaos， mix with and reinforce the traditional methods of applied mathematics. Thus， the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses.此书为英文版。

暂缺《偏微分方程的数值方法》作者简介

SeriesPreface
Preface
ContentsofPart2:ConservationLawsand
EllipticEquations
0Prelude
1IntroductiontoFiniteDifferences
1.1Introduction
1.2GettingStarted
1.2.1Implementation
1.3Consistency
1.3.1SpecialChoiceofAxandAt
1.4NeumannBoundaryConditions
1.5SomeVariations
1.5.1LowerOrderTerms
1.5.2NonhomogeneousEquationsand
BoundaryConditions
1.5.3AHigherOrderScheme
1.6DerivationofDifferenceEquations
1.6.1NeumannBoundaryConditions
1.6.2CellAveragedEquations
1.6.3CellCenteredGrids
1.6.4NonuniformGrids
SomeTheoreticalConsiderations
2.1Introduction
2.2Convergence
2.2.1Initial-ValueProblems
2.2.2Initial-Boundary-ValueProblems
2.2.3AReviewofLinearAlgebra
2.2.4SomeAdditionalConvergenceTopics
2.3Consistency
2.3.1Initial-ValueProblems
2.3.2Initial-Boundary-ValueProblems
2.4Stability
2.4.1Initial-ValueProblems
2.4.2Initial-Boundary-ValueProblems
2.5TheLaxTheorem
2.5.1Initial-ValueProblems
2.5.2Initial-Boundary-ValueProblems
2.6ComputationalInterludeI
2.6.1ReviewofComputationalResults
2.6.2HW0.0.1
2.6.3ImplicitSchemes
2.6.4NeumannBoundaryConditions
2.6.5DerivationofImplicitSchemes
Stability
3.1AnalysisofStability
3.1.1Initial-ValueProblems
3.1.2Initial-Boundary-ValueProblems
3.2FiniteFourierSeriesandStability
3.3GerschgorinCircleTheorem
3.4ComputationalInterludeII
3.4.1ReviewofComputationalResults
3.4.2HW0.0.1
ParabolicEquations
4.1Introduction
4.2TwoDimensionalParabolicEquations
4:2.1NeumannBoundaryConditions
4.2.2DerivationofDifferenceEquations
4.3Convergence,Consistency,Stability
4.3.1StabilityofInitial-ValueSchemes
4.3.2StabilityofInitial-Boundary-ValueSchemes
4.4AlternatingDirectionImplicitSchemes
4.4.1Peaceman-RachfordScheme
4.4.2Initial-ValueProblems
4.4.3Initial-Boundary-ValueProblems
4.4.4Douglas-RachfordScheme
4.4.5NonhomogeneousADISchemes
4.4.6ThreeDimensionalSchemes
4.5PolarCoordinates
HyperbolicEquations
5.1Introduction
5.2Initial-ValueProblems
5.3NumericalSolutionofInitial-ValueProblems
5.3.1OneSidedSchemes
5.3.2CenteredScheme
5.3.3Lax-WendroffScheme
5.3.4MoreExplicitSchemes
5.4ImplicitSchemes
5.4.1OneSidedSchemes
5.4.2CenteredScheme
5.4.3Lax-WendroffScheme
5.4.4Crank-NicolsonScheme
5.5Initial-Boundary-ValueProblems
5.5.1PeriodicBoundaryConditioos
5.5.2DirichletBoundaryConditions
5.6NumericalSolutionofInitial-Boundary-ValueProblems
5.6.1PeriodicBoundaryConditions
5.6.2DirichletBoundaryConditions
5.7TheCourantFriedrichs-LewyCondition
5.8TwoDimensionalHyperbolicEquations
5.8.1ConservationLawDerivation
5.8.2Initial-ValueProblems
5.8.3ADISchemes
5.8.4Courant-Friedrichs-LewyConditionfor
TwoDimensionalProblems
5.8.5TwoDimensionalInitial-Boundary-ValueProblems
5.9ComputationalInterludeIII
5.9.1ReviewofComputationalResults
5.9.2Convection-DiffusionEquations
5.9.3HW0.0.1
5.9.4HW0.0.2
SystemsofPartialDifferentialEquations
6.1Introduction
6.2Initial-ValueDifferenceSchemes
6.2.1FluxSplitting
6.2.2ImplicitSchemes
6.3Initial-Boundary-ValueProblems
6.3.1BoundaryConditions
6.3.2Implementation
6.4MultilevelSchemes
6.4.1ScalarMultilevelSchemes
6.4.2ImplementationofScalarMultilevelSchemes
6.4.3MultilevelSystems
6.5HigherOrderHyperbolicEquations
6.5.1Initial-ValueProblems
6.5.2More
6.6Courant-Friedrichs-LewyConditionforSystems
6.7TwoDimensionalSystems
6.7.1Initial-ValueProblems
6.7.2BoundaryConditions
6.7.3TwoDimensionalMultilevelSchemes
6.8SimultaneouslyDiagonalizableMatrices?
6.9AConsistent,Convergent,UnstableDifferenceScheme
6.10ComputationalInterludeIV
6.10.1HW0.0.1andHW0.0.2
6.10.2HW0.0.3
6.10.3ParabolicProblemsinPolarCoordinates
6.10.4AnAlternateSchemeforPolarCoordinates
7DispersionandDissipation
7.1Introduction
7.1.1HW5.6.3
7.1.2HW5.6.5
7.2DispersionandDissipationforPartial
DifferentialEquations
7.3DispersionandDissipationforDifferenceEquations
7.4DispersionAnalysisfortheLeapfrogScheme
7.5MoreDissipation
7.6ArtificialDissipation
7.7ModifiedPartialDifferentialEquation
7.8DiscontinuousSolutions
7.9ComputationalInterludeV
7.9.1HW0.0.1
7.9.2HW0.0.3
References
Index