21849.非線性滯時微分代數(shù)方程的穩(wěn)定性及隱式歐拉法的應用

1、學校代碼：10270學號：122200675分類號：O241.81碩士學位論文論文題目非線性滯時微分代數(shù)方程的穩(wěn)定性及隱式歐拉法的應用學院數(shù)理學院專業(yè)計算數(shù)學研究方向常微分方程數(shù)值解研究生姓名姜蘭蘭指導教師孫樂平完成日期二O—五年四月英文摘要上海師范大學碩士學位論文AbstractDifferentialalgebraicequations(DAEs)whichhasalgebraicconstraintsarisesinawideva

2、rietyofscientificengineeringapplicationsincludingrealtimesimulationcircuitanalysisoptimalcontrolcomputeraideddesignchemicalprocesssimulationmanagementsystem.Inmanycaseweshouldknowsomepaststatesofthesystemsoitconvertstoth

3、estudyofdelaydifferentialalgebraicequations(DDAEs).ThiskindofDDAEswithmecomplicatedstructurefithasnotonlydelaytermsbutalsothederivativesofdelayterms.itbecomesquitedifficulttoobtaintheanalyticsolutions.Therefeusingnumeric

4、almethodstosolvethiskindofsystemhasbecomeanimptantmeansthepremisefapplicationofnumericalmethodsistostudyvariouspropertiesoftheeticalsolutionwhichhasaveryimptanttheeticalpracticalsignificance.Inthispaperweinvestigateaclas

5、sofnonlineardelaydifferentialalgebraicequations.FirstSufficientconditionsfthetheyofstabilityasymptoticstabilityoftheequationsaregiven.ThenProofthattheseconditionscanbeappliedconvenientlytononlinearequations.Wealsoshowtha

6、ttheimplicitEulermethodsarestableasymptoticallystable.LastsomenumericalexperimentsarecarriedoutbyimplicitEulermethodstodemonstratetheconclusions.KeyWds:NonlineardelaydifferentialalgebraicequationImplicitEulermethodsstabi