带形无界域上具有neumann边界条件薛定谔方程有限元方法

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1、‘/Ã.·þäkNeumann>.^‡Å½™·§k··{Æž<'“6¶9…¡7U«Çƶ¡êƆOŽ‰ÆÆÆï‰Ä;·’·OŽêƇ©·§êŠ·{nØ9ÙA^Æž?OnÆa¬Æǃü‰ŒÆØ©JFÏ2011–4–20AfiniteelementmethodforSchr¨odingerequationwithNeumannboundaryconditionsinanunboundedstripCandidateSupervisorandRankJieLinProfessorJichengJinC

2、ollegeProgramMathematicsandComputationalScienceTheComputationalMathematicsSpecializationTheoryandApplicationsofNumericalMethodsforPDEsDegreeUniversityDateMasterofScienceXiangTanUniversityApr.20th,2011‰ÆØ©ŒÆM5(²

3、‡<½8N®²uL½>¤JŠ¬.é©ïĉÑ-‡z‡<Ú8N,þ®3©¥±²(·ªI².Šö¶:<¿£FÏ:(²{ÆcFJd<«ú.ÆØ©‡¦^ÇÖÆØ©Šö)Æk'3!¦^ÆØ©5½,Ó¿Æ3¿·I[k'Ü€½ÅxØ©E<‡Ú>f‡,#NØ©Ú/.<ljŒÆŒ±òÆØ©ܽܩSN?k'êâ¥?1u¢,Œ±æ^K.^‡Ž™

4、·§k··{?1ïÄ.·‚ÄkÏLÚ<ó>.^‡,rÃ.·þÐ>Š¯K=z·˜‡k.·þÐ>Š¯K,,éT¯K3žmþA^Crank-Nicolson©‚ª?1lÑ,3˜mþ^‚5½gk··{?1%C.²Lî‚nØ©Û,y²·‚¤ElÑ‚ª´Ã^‡-½ÚÂñ,¿ÙÂñ.·,‰Ñ˜‡êŠŽ~,`²·‚·{´k.'…i:Ž™·§;k··{;<ó>.^‡;Neumann>.^‡.IAbstractThisthesismainlydiscussesthefiniteelementmethodforSchr¨oding

5、erequationwithNeumannboundaryconditioninanunboundedstrip.First,wereducetheoriginalprob-lemintoaninitial-boundaryvalueprobleminaboundeddomainbyintroducinganartificialboundarycondition,andthenfullydiscretethisproblembyapplyingCrank-Nicolsonschemeintimeandlinearorquadratic

6、finiteelementapproximationinspace.Byarigorousanalysis,thisschemehasbeenprovedtobeunconditionallystableandconvergent,anditsconvergenceorderhasalsobeenobtained.Finally,wegiveanumericalexampletoverifytheaccuracyofthescheme.Keywords:Schr¨odingerequation;finiteelementmethod;

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