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525 个结果
  • 简介:Inthispaper,weconstructandanalyseamortarfinitevolumemethodforthediscretizationforthebiharmonicprobleminR2.Thismethodisbasedonthemortar-typeAdininonconformingfiniteelementspaces.TheoptimalorderH2-seminormerrorestimatebetweentheexactsolutionandthemortarAdinifinitevolumesolutionofthebiharmonicequationisestablished.

  • 标签: 双调和函数 离散化 有限元子空间 有限元法
  • 简介:AmutuallyorthogonalsystemofrationalSomeapproximationresultsareestablishedfunctionsonthewholelineisintroduced.Asanexampleofapplications,amodifiedLegendrerationalspectralschemeisgivenfortheDiracequation.Itsnumericalsolutionkeepsthesameconservationasthegenuinesolution.Thisfeaturenotonlyleadstoreasonablenumericalsimulationofnonlinearwaves,butalsosimplifiestheanalysis.Theconvergenceoftheproposedschemeisproved.Numericalresultsdemonstratetheefficiencyofthisnewapproachandcoincidewiththeanalysiswell.

  • 标签: 勒让德函数 光谱法 排列 近似值 单位脉冲函数
  • 简介:Inthispaper,wedealwiththeboundednessandtheasymptoticstabilityoflinearandone-legmultistepmethodsforgeneralizedpantographequationsofneutraltype,whicharisefromsomefieldsofengineering.Somecriteriaoftheboundednessandtheasymptoticstabilityforthemethodsareobtained.

  • 标签: 稳定性 有界性 渐进线 多级法
  • 简介:Inthispaper,weconsideraninversescatteringproblemforanobstacleDR^2withRobinboundarycondition.Byapplyingthepointsource,wegivearegularizingmethodtorecoverthescatteredfieldfromthefar-fieldpattern.Numericalimplementationsarealsopresented.

  • 标签: 反散射 点声源 规则化 数字化
  • 简介:ThispaperisconcernedwithnumericalmethodsforAmericanoptionpricing.Weemploynumericalanalysisandthenotionofviscositysolutiontoshowuniformconvergenceoftheexplicitdifferenceschemeandthebinomialtreemethod.Wealsoprovetheexistenceandconvergenceoftheoptimalexerciseboundariesintheaboveapproximn.tions.

  • 标签: 收敛 微分 二项式 数字分析 概率论
  • 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:Klein-Gordon-Schroedinger(KGS)equationsareveryimportantinphysics.Somepapersstudiedtheirwell-posednessandnumericalsolution[1-4],andanotherworksinvestigatedtheexistenceofglobalattractorinR^nandΩ包含于R^n(n≤3)[5-6,11-12].Inthispaper,wediscussthedynamicalbehaviorwhenweapplyspectralmethodtofindnumericalapproximationforperiodicinitialvalueproblemofKGSequations.ItincludestheexistenceofapproximateattractorAN,theuppersemi-continuityonAwhichisaglobalattractorofinitialproblemandtheupperboundsofHausdorffandfractaldimensionsforAandAN,etc.

  • 标签: KLEIN-GORDON-SCHROEDINGER方程 存在性 全局吸引子 谱逼近 SOBOLEV空间
  • 简介:Aderivativepatchinterpolatingrecoverytechniqueisanalyzedforthefiniteelementapproximationtothesecondorderellipticboundaryvalueproblemsintwodimensionalcase.Itisshownthattheconvergencerateoftherecoveredgradientadmitssuperconvergenceontherecoveredsubdomain,andistwoorderhigherthantheoptimalglobalconvergencerate(ultracovergence)ataninternalnodepointwhenevenorderfiniteelementspacesandlocaluniformmeshesareused.

  • 标签: 有限元逼近 超收敛性 偏微分方程 LAGRANGE插值
  • 简介:ThispaperpresentsthedualbasesforanewfamilyofgeneralizedBallcurveswithapositionparameterK,whichincludestheBeziercurve,generalizedSaid-Ballcurveandsomeintermediatecurves.Usingthedualbases,therelativeMarsdenidentity,conversionformulasofbasesandcontrolpointsofvariouscurvesareobtained.

  • 标签: BEZIER曲线 Marsden恒等式 SAID-BALL曲线 基底变换
  • 简介:Thepurposeofthispaperistostudythecascadicmultigridmethodforthesecondorderellipticproblemswithcurvedboundaryintwo-dimensionwhicharediscretizedbytheisoparametricfiniteelementmethodwithnumericalintegration.WeshowthattheCCGmethodisaccuratewithoptimalcomplexityandtraditionalmultigridsmoother(likesymmetricGauss-Seidel,SSORordampedJacobiiteration)isaccuratewithsuboptimalcomplexity.

  • 标签: 级联多栅法 等参有限元 数值积分 椭圆型方程
  • 简介:Inthispaper,theapplicationofhomotopymethodstotheloadflowmulti-solutionproblemsofpowersystemsisintroduced.BythegeneralizedBernshteintheorem,thecombinatorialnumberC2n^misshowntobetheBKKboundofthenumberofisolatedsolutionsofthepolynomialsystemtransformedfromloadflowequationswithgenericallychosencoefficients.AsaresultofthegeneralBezoutnumber,thenumberofpathsbeingfollowedisreducedsignificantlyinthepracticalloadflowcomputation.Finally,thecompleteP-Vcuresareobtainedbytrackingtheloadflowwithhomotopymethods.

  • 标签: 同伦法 电力系统 Bernshtein定理 负荷流动方程 Bezout数 非线性代数方程
  • 简介:Inthisarticleweconsiderthefullydiscretetwo-levelfiniteelementGalerkinmethodforthetwo-dimensionalnonstationaryincompressibleNavier-Stokesequations.ThismethodconsistsindealingwiththefullydiscretenonlinearNavier-StokesproblemonacoarsemeshwithwidthHandthefullydiscretelineargeneralizedStokesproblemonafinemeshwithwidthh<

  • 标签: 有限元GALERKIN法 NAVIER-STOKES方程 偏微分方程 时间离散化
  • 简介:Inthisarticleweconsideratwo-levelfiniteelementGalerkinmethodusingmixedfiniteelementsforthetwo-dimensionalnonstationaryincompressibleNavier-Stokesequations.ThemethodyieldsaH^1-optimalvelocityapproximationandaL^2-optimalpressureapproximation.Thetwo-levelfiniteelementGalerkinmethodinvolvessolvingonesmall,nonlinearNavier-StokesproblemonthecoarsemeshwithmeshsizeH,onelinearStokesproblemonthefinemeshwithmeshsizeh<

  • 标签: 有限元GALERKIN法 NAVIER-STOKES方程 空间离散化 偏微分方程 误差估计
  • 简介:Atwo-gridmethodforthesteadypenalizedincompressibleNavier-Stokesequationsispresented.Convergenceresultsareproved.Ifh=O(H^3-s)andε=O(H^5-2s)(s=0(n=2);s=1/2(n=3)arechosen,theconvergenceorderofthistwo-gridmethodisthesameasthatoftheusualfiniteelementmethod.Numericalresultsshowthatthismethodisefficientandcansavealotofcomputationtime.

  • 标签: NAVIER-STOKES方程 二格法 收敛性 有限元法
  • 简介:Inthispaper,wediscusstheconvergenceoftheBroydenalgorithmswithrevisedsearchdirection.Undersomeinexactlinesearches,weprovethatthealgorithmsaregloballyconvergentforcontinuouslydifferentiablefunctionsandtherateoflocalconvergenceofthealgorithmsisone-stepsuperlinearandn-stepsecond-orderforuniformlyconvexobjectivefunctions.

  • 标签: 修正BROYDEN算法 线搜索 收敛性 凸二次函数 步进因子
  • 简介:Inthispapertheleast-squaresmixedfiniteelementisconsideredforsolvingsecondorderellipticproblemsintwodimensionaldomains.Theprimarysolutionuandthefluxerareapproximatedusingfiniteelementspacesconsistingofpiecewisepolynomialsofdegreekandrrespectively.Basedoninterpolationoperatorsandanauxiliaryprojection,superconvergentH^1-errorestimatesofboththeprimarysolutionapproximationuhandthefluxapproximationσhareobtainedunderthestandardquasi-uniformassumptiononfiniteelementpartition.ThesuperconvergenceindicatesanaccuracyofO(h^r+2)fortheleast-squaresmixedfiniteelementapproximationifRaviart-ThomasorBrezzi-DouglasFortin-MarinielementsoforderrareemployedwithoptimalerrorestimateofO(h^r+l).

  • 标签: 超收敛性 最小二乘混合有限元法 椭圆型方程 近似解
  • 简介:Iterativetechniquesforsolvingoptimalcontrolsystemsgovernedbyparabolicvariationalinequalitiesarepresented.Thetechniquesweusearebasedonlinearfiniteelementsmethodtoapproximatethestateequationsandnonlinearconjugategradientmethodstosolvethediscreteoptimalcontrolproblem.Convergenceresultsandnumericalexperimentsarepresented.

  • 标签: 最优控制系统 抛物变分不等方程 有限元法 非线性共轭梯度法
  • 简介:Somenonlinearapproximants,i.e.,exponential-suminterpolationwithequaldistanceoratorigin,(0,1)-type,(0,2)-typeand(1,2)-typefraction-sumapproximations,formatrixvaluedfunctionsareintroduced.Alltheseapproximationproblemsleadtoasameformsystemofnonlinearequations.Solvingmethodsforthenonlinearsystemarediscussed.Conclusionsonuniquenessandconvergenceoftheapproximantsforcertainclassoffunctionsaregiven.

  • 标签: 非线性逼近 矩阵值函数 非线性方程 非线性系统 唯一性 收敛性
  • 简介:Inthispaper,weinvestigatetheoptimalityconditionsofaclassofspecialnonsmoothprogrammingminF(x)=∑mi=1|max{fi(x),ci}|whicharisesfromLl-normoptimization,whereci∈Risconstantandfi∈C^l,i=1,2,…,m.Theseconditionscaneasilybetestedbycomputer.

  • 标签: 非线性规划 最优性条件 广义梯度 方向导数