finite difference schemes and partial differential equations

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1、FiniteDifferenceSchemesandPartialDifferentialEquationsThispageintentionallyleftblankFiniteDifferenceSchemesandPartialDifferentialEquationsSecondEditionJohnC.StrikwerdaUniversityofWisconsin-MadisonMadison,WisconsinslamSocietyforIndustrialandAppliedMathematicsPhila

2、delphiaCopyright©2004bytheSocietyforIndustrialandAppliedMathematics.ThisSIAMeditionisasecondeditionoftheworkfirstpublishedbyWadsworth&Brooks/ColeAdvancedBooks&Software,PacificGrove,CA,1989.10987654321Allrightsreserved.PrintedintheUnitedStatesofAmerica.Nopartofthi

3、sbookmaybereproduced,stored,ortransmittedinanymannerwithoutthewrittenpermissionofthepublisher.Forinformation,writetotheSocietyforIndustrialandAppliedMathematics,3f.OOUniversityCityScienceCenter,Philadelphia,PA19104-2688.LibraryofCongressCataloging-in-PublicationD

4、ataStrikwerda,JohnC,1947-Finitedifferenceschemesandpartialdifferentialequations/JohnC.Strikwerda.—2nded.p.cm.Includesbibliographicalreferencesandindex.ISBN0-89871-567-91.Differentialequations,Partial—Numericalsolutions.2.Finitedifferences.I.Title.QA374.S882004518

5、'.64—dc2220040487145LLELJTLisaregisteredtrademark.ContentsPrefacetotheSecondEditionixPrefacetotheFirstEditionxi1HyperbolicPartialDifferentialEquations11.1OverviewofHyperbolicPartialDifferentialEquations11.2BoundaryConditions91.3IntroductiontoFiniteDifferenceSchem

6、es161.4ConvergenceandConsistency231.5Stability281.6TheCourant-Friedrichs-LewyCondition342AnalysisofFiniteDifferenceSchemes372.1FourierAnalysis372.2VonNeumannAnalysis472.3CommentsonInstabilityandStability583OrderofAccuracyofFiniteDifferenceSchemes613.1OrderofAccur

7、acy613.2StabilityoftheLax-WendroffandCrank-NicolsonSchemes763.3DifferenceNotationandtheDifferenceCalculus783.4BoundaryConditionsforFiniteDifferenceSchemes853.5SolvingTridiagonalSystems884StabilityforMultistepSchemes954.1StabilityfortheLeapfrogScheme954.2Stability

8、forGeneralMultistepSchemes1034.3TheTheoryofSchurandvonNeumannPolynomials1084.4TheAlgorithmforSchurandvonNeumannPolynomials117vviContents5DissipationandDispersi