邊值問題的微分求積法及其應(yīng)用.pdf

1、同濟大學(xué)理學(xué)院應(yīng)用數(shù)學(xué)系碩士學(xué)位論文邊值問題的微分求積法及其應(yīng)用姓名：任玉娥申請學(xué)位級別：碩士專業(yè)：計算數(shù)學(xué)指導(dǎo)教師：吳雄華20061201AbstractAbstractThedifferentialquadraturemethod(DQM)isanattractivenumericalmethodwithhighefficiencyandaccuracyButtheconventionalDQMislimitedinitsappli

2、cationt0regularregionsTodealwithproblemsonirregulargeometricd0_maiuscoordinatetransformationhastobeconductedThetriangulardifferentialquadraturemethod(TDQM)proposedbyZhong[4，6】avoidthecoordinatetransformationInthispaper，t

3、hedomaindecompositionmethod(DDM)isusedfortheelliptiealboundaryproblems0napentagonalregionIneverysubdomain，wesolvethepartialdifferentialequationswithTDQmethod，namelytriangulardifferentialquadraturedomaindecomposition(TDQD

4、D)methodWithboundaryreductiontechniquethefunctionalvaluesoninternalpointscanbeeliminatedThesystemofequationswhichsatisfiedbytheboundarypointscallbeobtainedNumeriealresultsshowthatiseasyandeffectivefortreatingtheproblemso

5、nirregularregionAnothersubjectisalsesearchedinthispaperThenumerica|differentiationisoftenusedwhendealiIlgwiththedifierentialequationsUsingthenumericaldifferentiation，thedifferentialequatiollscanbetransformedintoalgebraic

6、equ爭tionsThenwecangetthenumerical80lutionfromthealgebraicequationsButtheunmericaldifierentiationprocessisverysensitivetoevenasmaII1eveloferrolsIncontrastitisexpectedthatonaveragethenumericalintegrationprocessismuch1essse

7、nsitivetoerrorsInthispaperweprovideanewmethodusingtheDQmethodbasedontheinterpolationofthehighestderivative(DQIHD)forthedifferentiaIequationsT】艙originalfunctionisthenobtainedbyintegrationInthispaper，theDQIHDmethodwasappli

8、edtothebucklinganalysisofthinisotropicplates，thenumericalresultsshowthatouFmethodisofhighaccuracyofgoodconvergencewithlittlecomputationaleffortsAnditiseasytodealwiththeboundaryconditio璐Keywords：differentialquadraturemeth