一类八阶变系数微分方程的数值方法.pdf

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1、CHINESEJOURNALAug.2014Vol.31No.4OFENGINEERINGMATHEMATICSdoi:10.3969/j.issn.1005-3085.2014.04.014ArticleID:1005-3085(2014)04-0601-10NumericalMethodforaClassofEighth-orderDifferentialEquationswithVariableCoefficients∗XUChen-mei,MASong-ya(CollegeofMathematicsandInformationScience,HenanUniversi

2、ty,Kaifeng475001)Abstract:Inthisarticle,afinitedifferenceschemeforaclassofeighth-orderdifferentialequationswithvariablecoefficientsisestablished.Theschemeisrewritteninamatrixform.Theconvergenceanduniquenessofthesolutiontotheschemeareprovedbymeansofthematrixeigenvalueandnormtheory.Anumericale

3、xampleshowsthatthemethodisveryeffectiveandsimpletoimplement.Inaddition,themethodcanbeappliedtothestudyofsomenonlineardifferentialequationsarisinginapp-lications.Keywords:differentialequationswithvariablecoefficients;finitedifferencescheme;conver-genceanduniqueness;totaltruncationerrorClassific

4、ation:AMS(2000)65L10;65L70CLCnumber:O241.84Documentcode:A1IntroductionItiswellknownthatalotofproblemsfrequentlyarisinginstructuralengineer-ing,fluidmechanicsandotherbranchesofphysicalsciencescanbemodeledbydifferentialequationswithvariablecoefficients[1-4].Forexample,whenalayeroffluidisheatedf

5、rombelowandsubjectedtotheactionofrotation,instabilitymaysetinasoverstability[5;6].Theinstabilitymaybemodeledasaneighth-orderdifferentialequa-tionwithappropriateboundaryconditions.Theanalyticsolutionstothedifferentialequationsinapplicationscannotbeobtained,andthenumericalapproximationsarere-q

6、uired.Inrecentyears,variousnumericalmethods[7-9]havebeenappliedtodifferentialequations.Butthefinitedifferencemethodisveryeffectiveandsimpletoimplementforsomespecialdifferentialequations.Thefinitedifferencemethodisoneofthepio-neermethodsofnumericalapproximationsandstillarewidelybeingused.Toil

7、lustrateReceived:19Oct2012.Biography:XuChenmei(Bornin1965),Female,AssociateProfessor.Accepted:12Aug2013.Researchfield:numericalsolutionofdifferentialequations.Foundationitem:TheNationalNaturalScienceFoundationofChina(61201253);theNaturalScienceFoundationo