常微分方程邊值問題解的構造性證明及其計算.pdf

1、中國石油大學（華東）碩士學位論文常微分方程邊值問題解的構造性證明及其計算姓名：彭澤麗申請學位級別：碩士專業(yè)：計算數(shù)學指導教師：李維國20090501TheConstructiveProofandCalculationoftheSolutionsofBoundaryValueproblemofOrdinaryDifferentialEquationPengZeli(ComputationalMathematics)DirectedbyPr

2、o￡LiWeiguoAbstractThemaintopicofthispaperistheperiodicsolutionsofordinarydifferentialequationsPeriodicmovementsarecommonphenomenonofnatureandthefieldsofhumanactivitytheperiodicityproblemplaysacentralroleinthequalitativet

3、heoryofordinarydifferentialequationsAsallimportantaspectofapplication，findingperiodicsolutionsofordinarydifferentialequationsisanattractingtopicInthispaperwithinitialvalueproblemsmethod，aconstructiveproofofperiodicsoluti

4、onsofseveralspecialkindsofordinarydifferentialequationsisgivenMeanwhile，謝tlltheuseofthehomotophycontinuationmethod，someexamplesarecomputedThisapproachprovidesaglobalmethodforfindingperiodicsolutionsoftheseseveralkindsofe

5、quationsTheconstructiveproofofNewtonEquationandDuffingEquation、歷thpolarcoordinatesisgivenbyLiWeiguoTheadvantageofthismethodisthatithasawiderapplicationrange，buttheprocessofitsproofneedskillsanddifficulttostructureWegivea

6、constructiveproofofseveralspecialkindsofordinarydifferentialequationsforitsparticularThismethodisintuitive，simpleandeasytounderstand，butitsapplicationrangeisnarrowThispaperconsistsoffourchaptersInChapter1，weintroducethep

7、resentsituationoftheperiodicsolutionsofordinarydifferentialequationandfindingperiodicsolutionswithhomotophycontinuationmethodInChapter2，wediscusstheconstructiveproofgivenbyLi，InChapter3，wegiveaconstructiveproofforseveral

8、particularkindsofordinarydifferentialequationswimdifferentmethodInChapter4，weusethesanlemethodgivetheconstructiveproofofsemiperiodicsolutionsoftheequationswediscussinChapter3Keywords：OrdinaryDifferentialEquation，Periodic