分数阶微分方程配置方法

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2、nÆEÆ2i80/C12F2UY/~5*l2009–4–29CollocationMethodsforFractionalDifferentialEquationsCandidateXiangLiuSupervisorandRankProfessor.XuenianCaoCollegeMathematicsandComputationalScienceProgramComputationalMathematicsSpecializationNumericalMeth

3、odsforFractionalDifferentialEquationsDegreeMasterofScienceUniversityXiangTanUniversityDateApril29th,2009A)D4
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16、nÆE7;%%ws%kÆIAbstractThefractionaldifferentialequationshavebeenextensivelyappliedintheareasofmodernscientifictechniqueandengineering,suchasviscoelaseticmechanics,hydrogra-phy,Fractaldynamics,hydrodynamics,diffusionandtranspor

17、tandbioengineering.Thestudyofnumericalmethodsforthefractionaldifferentialequationsisbooming.Thereforetheresearchofnumericalmethodofthefractionaldifferentialequationisofimportanttheoricalsignificanceandpracticalvalue.Thisthesisisorganizedasfourchapters.Inchapter2,adetaileddescriptionofthecollocationm

18、ethodoflinearfractionalordinarydifferentialequationisgiven.Theconsistency,convergencyandstabilityanalysisofthemethodarealsoprovided.Inchapter3,thecollocationmethodofsolvingnonlinearfractionaldifferentialequationanditscorrespondingconsistenceandstabilityanalysisaregiven.InChapter4,numericalresultssh

19、owingthatourmethodsisefficient.Thelastpartofthearticle,wecarryonsummary’scombinetothistexttoputforwardtheoutlooktotheworkofthefuture.Keywords:Thefractionaldifferentialequation;convergence;consistency;stability;collocation