重構(gòu)核無網(wǎng)格方法及其誤差估計.pdf

1、東北大學碩士學位論文重構(gòu)核無網(wǎng)格方法及其誤差估計姓名：陶桂洪申請學位級別：碩士專業(yè)：基礎(chǔ)數(shù)學指導教師：宋叔尼20051201查韭苧鱟塑主堂堡墮查壘!坐型ReproducingKernelMeshfreeMethodandErrorEstimateAbstractAsanewnumericalmethod，meshfreemethodisrapidlydevelopedandoneofthehottestresearchareasover

2、theworldItcaneliminate，atleastpartlythemeshandavoidthedependencyofmeshsuchasfmiteelementmethodFirst，theprincipleofreproducingkernelmethodandtheconstructingmethodofapproximatewasintroducedAnewreproducingkernelleastsquarem

3、eshfreemethodWaspresentedbasedontheprincipleofpointleastsquaremethodandreproducingkernelmethodTherearetwonumericalexamplesonpartialdifferentialequations，oneisonedimensionandtheotheristwoCompilingmatlabcodeandsolvingnonli

4、nearequationsetwithNewtonmethodItisasimpleandhighconvergenceratemethodSecond，theerrorestimateofleastsquaremeshffeemethodforoneorderlineardifferentialoperatorisgotbasedontheerrorestimateofreproducingkernelapproximationand

5、leastsquaremethodParticularlyiftheoperatoriscoerciveandelliptic，theresultisshowninL2spacebyNitsche硎ckAboutthenonlineardifferentialoperatorwhichpreservesstronglymonotoneandLipschitzcontinuity，theresultissimilarUndersomeco

6、nditions，theerrorestimateofRKPMispresentedforsomenonlinearellipticboundaryproblemnirdbecausekernelfunctionisalSOanimportantroleinmeshfreemethodSplinesaresuitedfortheirpolynomialformsThroughthenumericalexample，theresultis

7、notbeaeraStheorderbecomeshigherThecomparisonfordifferentkemelfunctionsiSexhibitedinafigureIfotherconditionsarethesame，oneisuniformconvergence，theotherjsnotstable，Last，theinfluenceofpenaltyisnotnegleetedforthemethodintrod

8、ucedinthispaperForthelinearboundaryproblem，thereisnomuchimprovementonprecisionTheresultbecomesbeRerasthepenaltyfunctionisbigenoughfornonlinearboundaryproblemKeywordsmeshfreemethod，eiTorestimate，reproducingkernelapproxima