熱傳導(dǎo)方程Neumann邊界值問題的緊差分格式.pdf

1、東南大學(xué)碩士學(xué)位論文熱傳導(dǎo)方程Neumann邊界值問題的緊差分格式姓名：姜明杰申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：孫志忠20060222AbstractwYLiaoandJPZhu(J，Comp。Math，(2005))derives8highorderdifferenceschemeforthefollowingonedimensionalheatequation警=窘，(螂t≤z警m)_啉籌(1忙蹴otsT塒扛，0)=鐘o(z

2、)，0z1buttherei8notheoreticalanalysisInthispaperweprovethattheschemeisunconditionallystable，andisconvergentwiththeconvergenceorderofo(丁2≯5)Moreover，weimprovetheschemeandderiveamoreaccurateditiereiceschemebyreducingtheerro

3、rproducedbydiseretizationattheboundariesWealsoprovethatitisabsolutelystableandconvergentwiththeconvergenceorderof0—2h4)NumericalexamplestestifythetheoreticalresultsInthesecondpartwestudytheonedimensionalheatequationwithN

4、eumannboundaryconditionsbythemethodofreductionoforderandKellerBoxschemeByintroducing8newvariable口=Ⅱk，weeliminatetheerrorproducedbythediscretizationforthederivativeonboundaries，deriveafourthorderdi＆rencescheme，andanalyzee

5、xistenceuniqueness，convergenceandstabihtyofdifferencesolutionAnumericalexampledemonstratesthetheoreticQresultsKeywords：heatequation，Neumannboundaryvalue，boxscheme，methodofreductionoforder，mixedfinitevolume，existence，uniq