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1、2010–5–25StabilityAnalysisforNonlinearFunctionalDifferentialandFunctionalEquationswithVariableDelayCandidateSupervisorCollegeProgramJiangChunhuaProfessorYuYuexinMathematicsandComputationalScienceComputationalMathematicsSpecializationDegreeUniversityDateTheoryandApp
2、licationofNumericalMethodsforStiffDifferentialEquationsMasterofScienceXiangtanUniversityMay25,2010(FDEs),,,,,BanachVolterra(VFDEs)Runge-KuttaB-,B-,Volterra,(FDFEs),B-,FDFEs,(1)B-,FDFEs,FDFEs,Runge-KuttaB-(2)Runge-KuttaFDFEs,B-B-:B-,Runge-Kutt
3、aB-B-B-IAbstractFunctionaldifferentialequations(FDEs)arisewidelyinphysics,biology,engineering,medicalscience,economicsandsoon.ItismeaningfultostudythetheoryandapplicationofnumericalmethodsforFDEs.Inthelastseveraldecades,manyimportantresultsonthetheoryofcomputation
4、almethodsforFDEshavebeenreportedbyalargenumberofresearchers.Especially,thegeneralstabilitytheoryandB-theoryofnumericalmethodsincludingRunge-kuttamethodsandgenerallinearmethodsfornonlinearstiffVolterrafunctionalequations(VFDEs)inBanachspaceshasbeenestablishedbyLiShouf
5、oinrecentyears,whichprovidesaunifiedtheoreticalfoundationforthestabilityofthetheoreticalsolutionandB-stabilityandB-convergenceofnumericalmethodsfornonlinearstiffproblemsindelaydifferentialequations(DDEs),integro-differentialequations(IDEs),delay-integro-differentialequat
6、ions(DIDEs)andVFDEsofothertypesthatappearinpractice.However,thatworkisn’tadaptedfornonlinearneutralFDEs.FDEs,aclassofhybridsystems,whichconsistoffunctionaldifferentialequationandfunctionalequationandaremoreextendedthanneutralfunctionaldifferentialequation.Discussingth
7、etheoreticalsolutionandnumericalmethodsaremorecomplexthanotherfunctionaldifferentialequations.Atpresent,severalauthorsonlyhaveinvestigatedtheasymptoticstabilityofnumericalmethodsforlinearFDFEs.Inviewofthis,thethesisinvestigatesthestabilityofthetheoreticalsolutionandB
8、-stabilityandB-convergenceofRunge-KuttamethodsforaclassofnonlinearFDFEswithvariabledelay.Themainresultsobtainedareasfollowed:(1)Weobtainth
