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  • 简介:Thispaperconsiderstheasymptoticstabilityanalysisofbothexactandnumericalsolutionsofthefollowingneutraldelaydifferentialequationwithpantographdelay.{x′(t)+Bxd(t)+Cx′(qt)+Dx(qt)=0,t>0,x(0)=X0,}whereB,C,D∈C^d×d,q∈(0,1),andBisregular.Aftertransformingtheaboveequationtonon-automaticneutralequationwithconstantdelay,wedeterminesufficientconditionsfortheasymptoticstabilityofthezerosolution.Furthermore,wefocusontheasymptoticstabilitybehaviorofRunge-Kuttamethodwithvariablestepsize.ItisprovedthataLstableRunge-Kuttamethodcanpreservetheabove-mentionedstabilityproperties.

  • 标签: 渐近性 稳定性 朗格矢量法 延迟 渐近稳定度 微分方程
  • 简介:Thispaperfirstpresentsthestabilityanalysisoftheoreticalsolutionsforaclassofnonlinearneutraldelay-differentialequations(NDDEs).Thenthenumericalanalogousresults,ofthenaturalRunge-Kutta(NRK)methodsforthesameclassofnonlinearNDDEs,aregiven.Inparticular,itisshownthatthe(k,l)-algebraicstabilityofaRKmethodforODEsimpliesthegeneralizedasymptoticstabilityandtheglobalstabilityoftheinducedNRKmethod.

  • 标签: Nonlinear stability NEUTRAL DELAY differential EQUATIONS
  • 简介:ImplicitRunge-Kuttamethodishighlyaccurateandstableforstiffinitialvalueproblem.ButtheiterationtechniqueusedtosolveimplicitRunge-Kuttamethodrequireslotsofcomputationalefforts.Inthispaper,weextendtheParallelDiagonalIteratedRungeKutta(PDIRK)methodstodelaydifferentialequations(DDEs).WegivetheconvergenceregionofPDIRKmethods,andanalyzethespeedofconvergenceinthreepartsfortheP-stabilityregionoftheRunge-Kuttacorrectormethod.Finally,weanalysisthespeed-upfactorthroughanumericalexperiment.TheresultsshowthatthePDIRKmethodstoDDEsareefficient.

  • 标签: 朗格法 估计 微分方程 收敛
  • 简介:1.IntroductionConsidertheinitialvalueproblemwhichisassumedtohaveauniquesolutiony(t)ontheinterval[0,+co).Forsolving(1.1),considerthes--stageimplicitRunge-Kutta(IRK)methodandthes-stagemono-implicitRunge-Kutta(MIRK)method{2,51swhereh)0isthestepsize,hi,c...

  • 标签: Ordinary differential EQUATIONS Mono-implicit RUNGE-KUTTA methods
  • 简介:在这篇论文,为解决单个延期的二拍子的圆舞连续性Runge-Kutta(TSCRK)方法的一个班微分方程(DDE)被介绍。方法被给的这的数字稳定性的分析。我们考虑二个不同盒子:(ⅰ)τ≥h,(ⅱ)τRunge-Kutta的h的地方,方法两个都是不变的。一些方法的Theabsolute稳定性区域被阴谋,数字例子显示出方法的效率。

  • 标签: 时滞微分函数 稳定性 连续性 RUNGE-KUTTA方法