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

1、學(xué)校代碼：10270學(xué)號(hào)：122200675分類號(hào)：O241.81碩士學(xué)位論文論文題目非線性滯時(shí)微分代數(shù)方程的穩(wěn)定性及隱式歐拉法的應(yīng)用學(xué)院數(shù)理學(xué)院專業(yè)計(jì)算數(shù)學(xué)研究方向常微分方程數(shù)值解研究生姓名姜蘭蘭指導(dǎo)教師孫樂(lè)平完成日期二O—五年四月英文摘要上海師范大學(xué)碩士學(xué)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