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1、2009–5–30ANewClassofEfficientNumericalMethodsforNonlinearStiffDifferentialEquationsCandidateLiLinhaiSupervisorProfessor.HuangYunqingCollegeProgramSpecialityDegreeUniversityDateMathematicsandComputationalScienceComputationalMathematicsNumericalMethodsforDifferentialEqu
2、ationsMasterofScienceXiangTanUniversityMay30,2009B-EBDFNewBDFNBDFkNBDFkB-kkEBDFk−1kB-EBDFk=2,3,...,8NBDFEBDFNBDFEBDFNBDFB-B-EBDFINBDFAbstractBasedonB-theoryofnumericalmethodsfornonlinearstiffdifferentialequations,wemodifytheexistingEBDFmethods,andconst
3、ructanewclassofefficientnumericalmethodswhichareknownasNewBDFmethodswithabbreviationNBDFs.ItisprovedthatthekstepNBDFmethodisB-consistentoforderkandconvergentoforderkintheclassicalsense,andhasthesameperfectnumericalstabilitypropertiesasthek-thorderEBDFmethod,wherek=2,3,
4、···,8.However,thek-thorderEBDFmethodhasanessentialdrawbackthatit’sB−consistencyorderisonelessthantheconvergenceorder.Fortunately,thisdrawbackisovercomebyourNewBDFmethodsconstructed.Theoreticalanalysisandnumericalexperimentsshowthatforsolvingnonlinearstiffproblemstheco
5、mputationalaccuracyandefficiencyofanNBDFmethodisusuallymuchhigherthanthecorrespondingEBDFmethodofthesameorder,thelatterusuallycausesorderreduction,buttheformerusuallyhasobservedordercloselyneartoitsB-consistencyorder.Therefore,wecanconcludethattheNBDFmethodsconstructed
6、inthepresentpaperareofimportanceinpractice.KeyWords:Nonlinearstiffdifferetialequations;B-theory;EBDFmethods;NBDFmethods;accuracyandstabilityanalysisII.............................................................................(I)Abstract...............................
7、..........................................(II).....................................................................(1)NBDF.......................................................(4).....................................................(7)..............................
8、..........................(12)...............................................................(14)..................................
