求解微分方程的高精度樣條差分方法.pdf

1、廣西民族大學碩士學位論文求解微分方程的高精度樣條差分方法姓名：劉利斌申請學位級別：碩士專業(yè)：計算數(shù)學指導教師：劉煥文20090301ABSTRACThlthisthesistheapplicationsofsplinefunctionsinthenumericalsolutionsofdifferentialequationsareintroducedinthefirstchapterTheninthesecondchapterabri

2、efdis—cussiontocubic，quartic，quintic，sexticpolynomialsplinefunctionsandthecorrespondingrelationshipbetweensplinesaregivenLocalinterpolationerrorbysplinesalsodiscussedInthethirdchapterbasedontheclassicalquarticsplinefunct

3、ions，asixthorderdifferenceschemeispresentedforsolvingthesingularly—perturbedboundaryvalueproblemwithconstantcoefficientsAtthesametime，anothernewdifferenceschemeisproposedbyusingsexticsplinefunctions，thetruncationerrorcan

4、reachtoO(h8)attheinteriornodalpointsandO(h5)attheendnodalpointsInthefourthchapterbasedontheclassicalquarticsplinefunctions，anewmethodisgivenforsolvingthetwopointboundaryvalueproblemwithNeumannboundaryconditionsThetrllnca

5、tione訂0fofthisnewmethodtodealwiththederivativescanreachO(h4)atleast，whiletheaccuracyoftheclassicaldifferenceschemeiSsecondorderonlyInthefifthchapterbyusingquarticsplinefunctions，wepresentanunconditionallystabledifference

6、schemetosolvethesecondorderlinearhyperbolicequations，andthetruncationerrorofthisschemeisD(薩h4)Atthesametime，inthesixthchaptertwohighsemidiscretemethodswithhighaccu—racytOsolvethehyperbolicequationsaregiven，andthetruncati

7、onerrorsofthetwomethodsareO(Ph4)andD(妒h4)，respectivelyAtlastintheseventhandeighthchapters，weconsiderthenumericalsolutionofaclassofparabolicequationsbasedonquarticsplinefunctionsFordifferentboundaryconditions，wewillgiveso