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1、SpringerSeriesin38ComputationalMathematicsEditorialBoardR.BankR.L.GrahamJ.StoerR.VargaH.YserentantBertilGustafssonHighOrderDifferenceMethodsforTimeDependentPDEWith94Figuresand12Tables123BertilGustafssonLedungsvägen2875440UppsalaSwedenbertil@stanford.eduISBN978-3-540-74992-9e-ISBN978-3-540-7499
2、3-6DOI10.1007/978-3-540-74993-6SpringerSeriesinComputationalMathematicsISSN0179-3632LibraryofCongressControlNumber:2007940500MathematicsSubjectClassification(2000):65M06©2008Springer-VerlagBerlinHeidelbergThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconc
3、erned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,
4、andpermissionforusemustalwaysbeobtainedfromSpringer.ViolationsareliabletoprosecutionundertheGermanCopyrightLaw.Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsan
5、dregulationsandthereforefreeforgeneraluse.Coverdesign:WMXDesignGmbH,HeidelbergTypesetting:bytheauthorusingaSpringerLATEXmacropackageProduction:LE-TEXJelonek,Schmidt&VöcklerGbR,LeipzigPrintedonacid-freepaper987654321springer.comPrefaceManybookshavebeenwrittenonfinitedifferencemethods(FDM),butthe
6、rearegoodreasonstowritestillanotherone.Themainreasonisthatevenifhigherordermethodshavebeenknownforalongtime,theanalysisofstability,accuracyandeffectivenessismissingtoalargeextent.Forexample,thedefinitionoftheformalhighorderaccuracyisbasedontheassumptionthatthetruesolutionissmooth,orexpresseddif
7、ferently,thatthegridisfineenoughsuchthatallvariationsinthesolutionarewellresolved.Inmanyapplications,thisassumptionisnotfulfilled,andthenitisinterestingtoknowifahighordermethodisstilleffective.Anotherproblemthatneedsthoroughanalysisisthec
