移動網(wǎng)格方法和層適應網(wǎng)格在幾類奇異攝動問題上的應用.pdf

1、湘潭大學碩士學位論文移動網(wǎng)格方法和層適應網(wǎng)格在幾類奇異攝動問題上的應用姓名：周琴申請學位級別：碩士專業(yè)：計算數(shù)學指導教師：陳艷萍湯濤20080501ABSTRACTSingularlyperturbedproblemsarearisingfromfieldssuchasfluidmechanicselasticityacousticsopticschemicalreactionoptimalcontroletc.Theacteristi

2、csofsuchproblemsarethatthedifferentialequationscontainperturbedparameterswhichcanreflectthephysicalacteroftheequationscanbeintroducedartificially.Thesolutionofsuchproblemschangesquicklyinsomelocalregionofthesolvingregion

3、.Movingmeshmethodlayeradaptedgridscansolvetheseproblemseffectively.Inrecentyearsmanyscholarsathomeabroadhaveachievedmanyimptantresultsfsuchproblems.Inthispaperwestudytheapplicationofmovingmeshmethodlayeradaptedgridsfseve

4、ralsingularlyperturbedproblemsbasedonseveralreferences.InthefewdWeintroducethebackgroundofsingularlyperturbedproblemsresearchstatusofmovingmeshmethodlayeradaptedgridsftheseproblemsthenintroducethepaper’swkbriefly.Themain

5、bodyiscomposedofthreeparts.InthefirstpartweconstructdifferenceschemeonmovingmeshofaclassofsingularlyperturbedproblemprovethatthenumericalsolutionofdifferenceschemeismethanfirstderconvergencebyRidsonextrapolation.Weimprov

6、etwoalgithmscomparetheaccuracyrunningtimeofthetwoalgithmsbynumericalexperiments.Intraditionalalgithmstheinitialmeshofmovingmeshesisunifmmesh.WechangeittoBSmeshwhichissuitablefthemodelproblemcomparetherunningtimeaccuracyu

7、nderthetwoconditionsbynumericalexperiments.WegettheresultthatBSmeshisbetterthanunifmmeshasinitialmeshinrunningtimeaccuracy.InthesecondpartweconstructCrankNicolsondifferenceschemeonmovingmeshfaclassofnonconstantsingularly

8、perturbedconvectiondiffusionproblemwithsourcetermintroducetheiterativemethodalgithmofmovingmesh.WecompareerronmovingmeshunifmmeshbynumericalexperimentsprovethatitcandecreasenumericaloscillationeffectivelythatusingCrankNi

9、colsondifferenceschemeonmovingmesh.InthelastpartWeconstructdifferenceschemeofanellipticsingularlyperturbedproblem.Usingdecompositionofsolutionweanalysiseachpartonsubregionsprovethatthenumericalsolutionofdifferenceschemei