dirac方程高效的多辛算法

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1、IIAbstractThispaperstudiesthesplit-stepmulti-symplecticalgorithmfornonlinearDiracequation.Multi-symplecticsplit-stepalgorithmiscombythesplit-stepalgorithmandmulti-symplectical-gorithmtostudythenonlinearDiracequation.ThebasicideaistosplitnonlinearDiracequationintolinearandnonlinearsub-proble

2、mswithsymplecticormulti-symplectstructure,andthenre-spectivelywithsymplecticschemeisusedtodiscretethem,gettheformatwithintegralsympletic,whichexplaintheuniversalityandeffectivenessofthesplit-stepmulti-symplecticalgorithms.Inthefirstchapter,wemainlyintroducetheresearchbackgroundofsomenumerical

3、methodsforthenonlinearDiracequationandhavebeenappliedtothesolutionoftheDiracequation,andthengivessomebasicsknowledgeofthisarticleneedtoknow.Inthesecondchapter,webeginadetailedstudyofthemulti-symplecticalgorithmfornonlin-earDiracequation.Firstconstructedmulti-symplecticstructuralofthenonline

4、arDiracequation,andthenusetheRunge-Kuttaformattodiscreteandnumericalsimulation.Nextapplyingsplit-stepalgorithmtotheDiracequation,constructasplit-stepmulti-symplecticalgorithmfornonlin-earDiracequation,andthenusingdifferentformatsdiscrete.Thefirstdiscretemethodisusethemidpointofdiscreteformatd

5、iscrete;Theseconddiscretemethodisusehigher-ordercompactfor-mattodiscreteinspace,timewithsymplecticEulermethodofdiscrete,andanalyzethestabilityofconditionalofscheme.Finally,throughnumericalexperimentscomparewiththetraditionalmulti-symplecticalgorithms,reflectingtheadvantagesofsplit-stepmulti-

6、symplecticalgorithmsforfurtheranalysis.Inthethirdchapterthesplit-stepmulti-symplecticalgorithmsisextendedtononlineartwo-dimensionalnonlinearDiracequation,analysisthestabilityofcondition,thefinalnumericalex-periments,analyzethefeasibilityoftheirapproach.Inthefourthchapter,abriefsummaryoftheco

7、ntentofthispaper.thenputsforwardthetentativeideaoffurtherstudyonnonlinearDiracequation.Keywords:Diracequation;split-stepmethod;highordercompactscheme;conservationIIIIV目录摘要I英文摘要III第一章引言1第二章一维Dirac方程的分裂步多辛格式72.1Dirac方程的多辛Runge-Kutta格式......................