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简介：Thispaperpresentsthestabilityofdifferenceapproximationsofanoptimalcontrolproblemforaquasilinearparabolicequationwithcontrolsinthecoefficients,boundaryconditionsandadditionalrestrictions.Theoptimalcontrolproblemhasbeenconveredtooneoftheoptimizationproblemusingapenaltyfunctiontechnique.Thedifferenceapproximationsproblemfortheconsideredproblemisobtained.Theestimationsofstabilityofthesolutionofdifferenceapproximationsproblemareproved.Thestabilityestimationofthesolutionofdifferenceapproximationsproblembythecontrolsisobtained.

简介：Inthispaper,wedealwiththeboundednessandtheasymptoticstabilityoflinearandone-legmultistepmethodsforgeneralizedpantographequationsofneutraltype,whicharisefromsomefieldsofengineering.Somecriteriaoftheboundednessandtheasymptoticstabilityforthemethodsareobtained.

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.

简介：SymplecticintegrationofseparableHamiltonianordinaryandpartialdifferentialequationsisdiscussed.AvonNeumannanalysisisperformedtoachievegenerallinearstabilitycriteriaforsymplecticmethodsappliedtoarestrictedclassofHamiltonianPDEs.Inthistreatment,thesymplecticstepisperformedpriortothespatialstep,asopposedtothestandardapproachofspatiallydiscretisingthePDEtoformasystemofHamiltonianODEstowhichasymplecticintegratorcanbeapplied.InthiswaystabilitycriteriaareachievedbyconsideringthespectraoflinearisedHamiltonianPDEsratherthanspatialstepsize.

简介：Thispaperfirstpresentsthestabilityanalysisoftheoreticalsolutionsforaclassofnonlinearneutraldelay-differentialequations(NDDEs).Thenthenumericalanalogousresults,ofthenaturalRunge-Kutta(NRK)methodsforthesameclassofnonlinearNDDEs,aregiven.Inparticular,itisshownthatthe(k,l)-algebraicstabilityofaRKmethodforODEsimpliesthegeneralizedasymptoticstabilityandtheglobalstabilityoftheinducedNRKmethod.

简介：Thispaperdealswithanalyticandnumericaldissipativityandexponentialstabilityofsingularlyperturbeddelaydifferentialequationswithanyboundedstate-independentlag.Sufficientconditionswillbepresentedtoensurethatanysolutionofthesingularlyperturbeddelaydifferentialequations(DDEs)withaboundedlagisdissipativeandexponentiallystableuniformlyforsufficientlysmallε>0.Wewillstudythenumericalsolutiondefinedbythelinearθ-methodandone-legmethodandshowthattheyaredissipativeandexponentiallystableuniformlyforsufficientlysmallε>0ifandonlyifθ=1.

简介：Thispaperdealswiththeasymptoticstabilityanalysisofθ-methodsformultipantographdelaydifferentialequation{ú(t)=λu(t)+∑↑ιi=1μiu(qit),0

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)τ