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1、ONSPURIOUSASYMPTOTICNUMERICALSOLUTIONSOFGAUSSSCHEMELiuWenhaiFujianInternationalBusinessandEconomicCollegeAbstractInthispaper,wediscusscharacteristicsofGaussschemefornumericalordinarydifferentialequations,whichisaone-stephigh-orderaccuratedifferencescheme.Weapplysuchschemetosomeequations,anda
2、nalyzethefixedpointandstabilityaccordingly.Keywords:Ordinarydifferentialequations，differencescheme，stability，fixedpoint１ IntroductionFormostoftheordinarydifferentialequations,theiranalyticalexpressionsarenoteasilyidentified.Occasionally,eveniftheclosedformofsolutionscanbefound,thesesolutions
3、turnouttobeimpracticalbecauseofthelargeamountofcalculationinvolved.Undersuchcircumstancesnumericalmethodsareintroducedtosolveordinarydifferentialequations.Withregardtothenumericalschemeofordinarydifferentialequations,[[]H.C.Yee,P.K.Sweby,SomeAspectsofNumericalUncertaintiesinTimeMarchingtoSte
4、ady-StateComputations,AIAA-96-2052,27thAIAAFluidDynamicsConference,June18-20,1996,NewOrleans,LA,AIAAJ.,36(1998),712-724.]thesolutionofdifferentschememaybecomeperiodic,chaotic,anddivergentoncethesteplengthexceedsitsstableboundary.Forexample,usinganexplicitEulerdifferenceschemetosolvethefollow
5、ingordinarydifferentialequations（１.１） Weobtaindifferentequations（１.２） Hereweletｈdenotethetimestepofdifferentscheme,.Ifｒ<2and(1.2)isconvergent,thesolutionsto(1.2)areconvergentto1,whichisthefixedpointoftheordinarydifferentialequation(1.1).If２£ｒ£２.43,thesolutionsof(1.2)possessdoubleperi
6、odicity;If2.43<ｒ<3,thesolutionsof(1.2)havemultipleperiodicitychaosphenomenon.Ifｒ³3,thesolutionsto(1.2)dissipatesasaresult.Thispaperaimstoconstructtheone-stepexplicitdifferentschemeofordinarydifferentialequation(1.1),usingGAUSStypeintegrationformula.Furthermore,thedifferentschemeobtainedisapp
7、liedtotheecologicalcommunitygrowthmodel,[[]B.Sjögreen,H.C.Yee,LowDissipativeHighOrderNumericalSimulationsofSupersonicReactiveFlows,RIACSReport01-017,NASAAmesresearchcenter,May2001,ProceedingsoftheECCOMASComputationalFluidDynamicsConference2001,Swan
