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1、Banach2012-04-20StabilityAnalysisofaClassofMultistepMethodsforNonlinearFunctionalDifferentialandFunctionalEquationsinBanachSpaceCandidateSupervisorandRankSonglinFangProfessorYuexinYuCollegeProgramSpecializationDegreeUniversityMathematicsandComputationalScienceComputatio
2、nalMathematicsTheoryandApplicationofNumericalMethodsforStiffDifferentialEquationsMasterofScienceXiangtanUniversityDateApril202012.(FDFEs)LipschitzLipschitzLipschitzBanachBanachBanachDλ∗(α,β1,β2,γ1,γ2,γ3,µ1,µ2)Dλ∗,δ(α,β1,β2,γ1,γ2,γ3,µ1,µ2),D0(α,β1,β2,γ1,γ2,γ3,µ1,µ2)Banac
3、hDλ∗(α,β1,β2,γ1,γ2,γ3,µ1,µ2)Dλ∗,δ(α,β1,β2,γ1,γ2,γ3,µ1,µ2)BanachILipschitzAbstractFunctionaldifferentialandfunctionalequations(FDFEs)aremorecomplexthanFDEs.Theyareaclassofhybirdproblemformedbyfunctionaldifferentialequationsandfunctionalequations.However,thereexistslotsofs
4、tiffproblemsinscienceandengineering,despitethewholequestionitselfisgoodstate,whenusingthecorrespondingnormofinnerproduct,itmayhappenthattheone-sidedLipschitzconstantisaverylargepositivenumber.Therefore,itisurgentandmeaningfultobreaktherestrictionofthecorrespondingnormofin
5、nerproductandtheone-sidedLipschitzconstanttostudythenumericaltheoryinBanachspace.Inviewofthis,thispaperalsoresearchdirectlyaclassoftheinitialvalueproblemsofnonlinearfunctionaldifferentialandfunctionalequationsinBanachspaces.Firstofall,weintroducetestproblemclassesDλ∗(α,β1
6、,β2,γ1,γ2,γ3,µ1,µ2)andDλ∗,δ(α,β1,β2,γ1,γ2,γ3,µ1,µ2)withrespecttotheinitialvalueproblemsofnonlinearfunctionaldifferentialandfunctionalequationsinBanachspaces.AseriesofstabilityresultsoftheanalyticsolutionareobtainedandaconditionestimatefortheclassD0(α,β1,β2,γ1,γ2,γ3,µ1,µ2)
7、whichbasedonlogarithmicmatrixnormisalsoobtained.Second,aseriesofnewstabilitycriteriasofthevariablecoefficientlinearmultistepmethodswhenappliedtothetestproblemclassesDλ∗(α,β1,β2,γ1,γ2,γ3,µ1,µ2)andDλ∗,δ(α,β1,β2,γ1,γ2,γ3,µ1,µ2)arees-tablishedinBanachspace.Finally,Numericaltes
8、tshavegiventoconfirmthetheoreticalresults.KeywordFunctionaldifferentialandfunctionalequations;Banachspace
