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、華中科技大學碩士學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：董點申請學位級別：碩士專業(yè)：計算數(shù)學指導教師：黃乘明20061001華中科技大學碩士學位論文華中科技大學碩士學位論文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