关于延迟微分方程二级lobatto+iiic+runge-kutta法若干注记

《关于延迟微分方程二级lobatto+iiic+runge-kutta法若干注记》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、LobattoIIICRunge-KuttaSomenotesoftwostageLobattoIIICRunge-KuttamethodfordelaydifferentialequationsCandidateSupervisorandRankBinZhangProf.Shou-fuLiCollegeProgramMathematicsandComputationalScienceTheComputationalMathematicsSpecializationNumericalMethodsforFunctionalDifferentialEquationsandFluid

2、DegreeUniversityDateMasterofScienceXiangTanUniversityApril22th,2011::.,.:..,,,.,..::::(DDEs)VolterraB-B-,BellenNumericalmethodsfordelaydifferentialequations2LobattoIIICRunge-KuttaB-Bellen1DDE2LobattoIIICRunge-Kutta(Lobatto2)DDE2LobattoIIICRadauIIAGaussRunge-KuttaLobatto2.

3、Lobatto2RadauIIAGauss2LobattoIIICRunge-Kutta:IIICRunge-Kutta;B-.;;;LobattoIAbstractThefirstpartofthepaperstudiesconstantcoefficientlinearscalardelaydifferentialequations,andprovesbothimplicitmid-pointmethodandtrape-zoidalruleisB-stableandconditionallycontractive.Furthermore,thesameconclusi

4、oncanbesimilarlypromotedforaclassofvariablecoefficientsemi-linearscalarVolterrafunctionaldifferentialequations.ThetwoexamplesBellenmen-tionedinthechapter1ofthebookNumericalmethodsfordelaydifferentialequationsindicatedthat2stageLobattoIIICRunge-Kuttamethodisagoodmethodwhileneithermid-pointmethodn

5、ortrapezoidalruleisB-stable.Theconclusionisalittledefective.Infact,thetwomethodsaboveareB-stableandconditionallycontractiveforsolvingthetwoexamplesgiveninthefirstchapterofBellen’sbook,onlyifthestepsizeoftheexamplesisdecreasedappropriately.What’smore,theresultofsolvingtheprobleminexample1indica

6、testhepracti-calcalculationefficiencyofbothimplicitmid-pointmethodandtrapezoidalruleismuchhigherthan2stageLobattoIIICRunge-Kuttamethod(Lobatto2).ThesecondpartofthispaperstudiesthegeneralnonlinearsitffDDEs,andcomparesthe2stageRunge-KuttamethodssuchasLobattoIIIC,RadauIIAandGauss.Boththeoreticalana

7、lysisandnumericalexperimentationsindicatethattheabovethreemethodscostalmostidenticaltimeineveryintegralstep,butthecomputationalaccuracyofthelattertwomethodsismuchhigherthanLobatto2.ItisseenfromtheabovethatLobatto2isnotworthtoberecommended.Wes