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1、PhysicaD165(2002)6693AsymptoticanalysisoftworeductionmethodsforsystemsofchemicalreactionsHansG.Kapera,∗,TassoJ.KaperbaMathematicsandComputerScienceDivision,ArgonneNationalLaboratory,Argonne,IL,USAbDepartmentofMathematicsandCenterforBioDynamics,BostonUniversity,Boston,MA,USAReceived26October200
2、1;receivedinrevisedform6February2002;accepted11February2002CommunicatedbyC.K.R.T.JonesAbstractThispaperconcernstwomethodsforreducinglargesystemsofchemicalkineticsequations,namely,themethodofintrinsiclow-dimensionalmanifolds(ILDMs)duetoMaasandPope[Combust.Flame88(1992)239]andaniterativemethoddu
3、etoFraser[J.Chem.Phys.88(1988)4732]andfurtherdevelopedbyRousselandFraser[J.Chem.Phys.93(1990)1072].Bothmethodsexploittheseparationoffastandslowreactiontimescalestofindlow-dimensionalmanifoldsinthespaceofspeciesconcentrationswherethelong-termdynamicsareplayedout.Theasymptoticexpansionsoftheseman
4、ifolds(ε↓0,whereεmeasurestheratioofthereactiontimescales)arecomparedwiththeasymptoticexpansionofMε,theslowmanifoldgivenbygeometricsingularperturbationtheory.ItisshownthattheexpansionsoftheILDMandMεagreeuptoandincludingtermsofO(ε);theformerhasanerroratO(ε2)thatisproportionaltothelocalcurvatureo
5、fM0.Theerrorvanishesifandonlyifthecurvatureiszeroeverywhere.Theiterativemethodgenerates,termbyterm,theasymptoticexpansionofMε.StartingfromM0,theithapplicationofthealgorithmyieldsthecorrectexpansioncoefficientatO(εi),whileleavingthelower-ordercoefficientsinvariant.Thus,afterapplications,theexpan
6、sionisaccurateuptoandincludingthetermsofO(ε).Theanalyticalresultsareillustratedonaplanarsystemfromenzymekinetics(MichaelisMentenHenri)andamodelplanarsystemduetoDavisandSkodje.©2002PublishedbyElsevierScienceB.V.MSC:80A30;34E13;92C45;34C20;34E15PACS:05.45.−a;05.10.−a;82.20;82.33.V;87.15.R;82.33
7、.T;02.60.LjKeywords:Chemicalkinetics;Combustion;Atmosphericchemistry;Enzymekinetics;Biophysics;Reductionmethods;Slowmanifolds;Intrinsiclow-dimensionalmanifolds;Geometricsingularperturbationtheory;Multipletimescales;Asymptoticanalysis;Mi
