非线性延迟积分微分方程数值方法稳定分析

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1、2009–10–28StabilityAnalysisofNumericalMethodsforNonlinearDelayIntegro-differentialEquationsCandidateSupervisorCollegeProgramSpecialityDegreeUniversityDateChenZhigangDr.YuYuexinMathematicsandComputationalScienceAppliedMathematicsTheoryandApplicationofNumericalMethodsforStiffDifferentialEqua

2、tionsMasterofScienceXiangTanUniversityOctober28,2009(1)()A-A-(2)A-A-IAbstractDelayintegro-differentialequations(DIDEs)arisewidelyinthefieldsofphysics,biology,chemistry,medicine,economics,controltheoryandsoon.ItismeaningfultoinvestigatethetheoryandapplicationofnumericalmethodsforDIDEs.Inr

3、ecent30years,thetheoryofcomputationalmethodsforDIDEshasbeenwidelydiscussedbymanyauthorsandagreatdealofresultshavebeenfound.ThepapersaremainlyfocusedonthelinearsystemsofDIDEs,andafewpapersstudythenumericalstabilityofnonlinearDIDEs.Thepresentpaperisdevotedtothestabilityanalysisofnumericalm

4、ethodsfornonlinearDIDEs.Themainresultsobtainedareasfollows.(1)One-legmethodsareadaptedforsolvingaclassofnonlinearDIDEs.ItisprovedthatanA-stableone-legmethodsisnumericallystableandastronglyA-stableone-legmethodsisasymptoticallystableunderthesuitableconditions.Numericaltestsaregiventoconfir

5、mthetheoreticalresults.(2)LinearmultistepmethodsareadaptedforsolvingaclassofnonlinearDIDEs.ItisprovedthatanA-stablelinearmultistepmethodsisasymptoticallystableunderthesuitableconditions.Numericaltestsaregiventoillustratethetheoreticalresults.Keywords:Nonlineardelayintegro-differentialequa

6、tions,numericalsta-bility,asymptoticstability,A-stability,one-legmethods,linearmultistepmeth-ods.II................................................1§1.1§1.2§2.1§2.2§2.3§3.1§3.2§3.3..............................................1............................................4...............

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