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1、θ−2009–5–28StabilityAnalysisofθ−methodsforFunctionalDifferentialandFunctionalEquationsCandidateSupervisorCollegeProgramSpecialityDegreeUniversityDateZhangZhuofeiDr.YuYuexinMathematicsandComputationalScienceComputationalMathematicsTheoryandApplicationofNumericalMethodsforStiffDiff
2、erentialEquationsMasterofScienceXiangTanUniversityMay28,2009(1)θ-()θ-1/2≤θ≤1(2)θ-1/2<θ≤1θ-1/2≤θ≤1θ−Iθ−AbstractFunctionaldifferentialequations(FDEs)arisewidelyinthefieldsofcon-troltheory,physics,biology,medicine,chemistry,economicsandsoon.Itismeaningfultoinvestigatethetheo
3、ryandapplicationofnumericalmethodsforFDEs.Inrecent30years,thetheoryofcomputationalmethodsforFDEshasbeenwidelydiscussedbymanyauthorsandagreatdealofresultshavebeenfound.Functionaldifferentialandfunctionalequations(FDFEs)areaclassofhybridsystemsthataremorecomplexthanthatofFDEs.Inpa
4、rticular,func-tionaldifferentialequationsofneutraltypecanbetransformedintoFDFEs.Thenumericalstabilityanalysisofneutralfunctionaldifferentialequationshasbeenstudiedextensivelyinrecentyears.AsforthesystemsofFDFEs,theasymptoticstabilityofnumericalmethodsforlinearFDFEshasbeendiscusse
5、dbyseveralauthors.However,littleattentionhasbeenfocusedonthenonlin-earsystemsofFDFEs.Forthesereasons,thepresentpaperisdevotedtothestabilityanalysisofnumericalmethodsfornonlinearFDFEs.Themainresultsobtainedareasfollows.(1)One-legθ−methodsareadaptedforsolvingaclassofnonlinearFDFE
6、s.Inisproventhatone-legθ−methodsarenumericallystablefor1/2≤θ≤1andasymptoticallystablefor1/2<θ≤1underthesuitableconditions.Numericaltestsaregiventoconfirmthetheoreticalresults.(2)Linearθ−methodsareadaptedforsolvingaclassofnonlinearFDFEs.Inisproventhatlinearθ−methodsareasymptotica
7、llystablefor1/2≤θ≤1underthesuitableconditions.Numericaltestsaregiventoillustratethetheoreticalresults.Keywords:Functionaldifferentialandfunctionalequations,neutraldelaydifferentialequations,numericalstability,asymptoticstability,one-legθ−methods,linearθ−methods.II................
8、................................1§1.1§1.2θ-.........
