求解微分方程的高精度樣條差分方法.pdf

1、廣西民族大學(xué)碩士學(xué)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(qǐng)學(xué)位級(jí)別：碩士專業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)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