兩類剛性微分方程一般線性方法的非線性穩(wěn)定性和誤差分析.pdf

1、華中科技大學(xué)碩士學(xué)位論文兩類剛性微分方程一般線性方法的非線性穩(wěn)定性和誤差分析姓名：董點申請學(xué)位級別：碩士專業(yè)：計算數(shù)學(xué)指導(dǎo)教師：黃乘明20061001華中科技大學(xué)碩士學(xué)位論文華中科技大學(xué)碩士學(xué)位論文IIAbstractStiffdifferentialequationsarewidelyusedinmanyfields.Manyscholarshavedevotedgreatenergyresearchtothemhaveachieve

2、dfruitfulresults.Inthefirstchapterwerecalltheiginofdelaydifferentialequationsthedevelopmentofthestudyoftheirnumericalstability.Thenweturnourattentiontosingularperturbationproblems(SPPs)whichareaspecialclassofstiffdinaryd

3、ifferentialequations(ODEs).Somenumericalmethodsrelatedconvergenceresultsarereviewed.Meanwhilewebrieflyintroducetheconvergencetheyofdinarydifferentialequationsfnumeicalmethods.Inthesecondchapterwediscussnonlinearstability

4、ofgenerallinearmethodsfvariabledelaydifferentialequations.UndertheassumptionthatthedelaysatisfiesLipschitzconditionwiththeminimumlipschitzconstantL1weobtainsomeresultsonthestabilityofgenerallinearmethodswithlinearinterpo

5、lationprocedure.Inthethirdchapterwediscussgenerallinearmethodsfsolvingaclassofmultiplystiffsingularperturbationproblems.OnthebasisofGan’sarticlewerelaxtherequirementofalgebraicstabilityundertheweaklyalgebraicdiagonalstab

6、ilityconditionsobtainedtheerrestimatesofgenerallinearmethods.Inthefourthchapterwediscussgenerallinearmethodofsolvingtwoparameterssingularperturbationproblems(SPPs).OnthebasisofthewkbyXiaoontheconvergenceofRungeKuttametho

7、dslinearmultistepmethodsftwoparametersSPPscombinedwiththeconvergenceresultsongenerallinearmethodsfoneparameterSPPsbyGanwefurtherobtainaglobalerrestimatefgenerallinearmethodsftwoparameterSPPs.Inthefifthchaptersomenumerica