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1、上海師范大學碩士學位論文DynamicsofLinearMultistepMethodsfDelayDifferentialEquations姓名:范利強申請學位級別:碩士專業(yè):計算數(shù)學指導教師:項家祥20050401AbstractDelaydiferentialdynamicalsystemshaveappearedinareasofapplicationsasdiverseasneuralnetworksopticsbiology
2、automaticcontroltheory.Therearemanysignificantachievementsonbasictheorystabilitytheoryperiodsolutiontheoryandbifurcationtheoryofdelaydiferentialsystems.Numericalsimulationisoneofthemostimportantmethodstounderstanddynamic
3、alpropertiesofdelaydiferentialequations.Anumericalmethodwhichisconvergentinafiniteintervaldoesnotyieldthesameasymptoticbehaviorastheunderlyingdiferentialequation.Thereforeitisveryimportanttoinvestigatethedynamicsofnumeri
4、calmethodsforsolvingdelaydiferentialequationsThepu印oseofthispaperistostudysomedynamicalpropertiesof0methodsandmultistepmethodssolvingdelaydiferentialequations.Itcontains①numericaldissipativityoflinear0methodandmultistepm
5、ethods①regularityoflinearmultistepmethodsand①stabilityofspuriousperiodtwosolutionoflinear0method.KeyWords:Delaydiferenticaldynamicalsystemdissipativityabsorbingsetregularityhyperbolicequilibriumasymptoticbehaviorspurious
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