简介：Inthispaper,weconstructandanalyseamortarfinitevolumemethodforthediscretizationforthebiharmonicprobleminR2.Thismethodisbasedonthemortar-typeAdininonconformingfiniteelementspaces.TheoptimalorderH2-seminormerrorestimatebetweentheexactsolutionandthemortarAdinifinitevolumesolutionofthebiharmonicequationisestablished.

简介：AmutuallyorthogonalsystemofrationalSomeapproximationresultsareestablishedfunctionsonthewholelineisintroduced.Asanexampleofapplications,amodifiedLegendrerationalspectralschemeisgivenfortheDiracequation.Itsnumericalsolutionkeepsthesameconservationasthegenuinesolution.Thisfeaturenotonlyleadstoreasonablenumericalsimulationofnonlinearwaves,butalsosimplifiestheanalysis.Theconvergenceoftheproposedschemeisproved.Numericalresultsdemonstratetheefficiencyofthisnewapproachandcoincidewiththeanalysiswell.

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

简介：Inthispaper,weconsideraninversescatteringproblemforanobstacleDR^2withRobinboundarycondition.Byapplyingthepointsource,wegivearegularizingmethodtorecoverthescatteredfieldfromthefar-fieldpattern.Numericalimplementationsarealsopresented.

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

简介：ThispaperisconcernedwithnumericalmethodsforAmericanoptionpricing.Weemploynumericalanalysisandthenotionofviscositysolutiontoshowuniformconvergenceoftheexplicitdifferenceschemeandthebinomialtreemethod.Wealsoprovetheexistenceandconvergenceoftheoptimalexerciseboundariesintheaboveapproximn.tions.

简介：ImplicitRunge-Kuttamethodishighlyaccurateandstableforstiffinitialvalueproblem.ButtheiterationtechniqueusedtosolveimplicitRunge-Kuttamethodrequireslotsofcomputationalefforts.Inthispaper,weextendtheParallelDiagonalIteratedRungeKutta(PDIRK)methodstodelaydifferentialequations(DDEs).WegivetheconvergenceregionofPDIRKmethods,andanalyzethespeedofconvergenceinthreepartsfortheP-stabilityregionoftheRunge-Kuttacorrectormethod.Finally,weanalysisthespeed-upfactorthroughanumericalexperiment.TheresultsshowthatthePDIRKmethodstoDDEsareefficient.

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.

简介：Aderivativepatchinterpolatingrecoverytechniqueisanalyzedforthefiniteelementapproximationtothesecondorderellipticboundaryvalueproblemsintwodimensionalcase.Itisshownthattheconvergencerateoftherecoveredgradientadmitssuperconvergenceontherecoveredsubdomain,andistwoorderhigherthantheoptimalglobalconvergencerate(ultracovergence)ataninternalnodepointwhenevenorderfiniteelementspacesandlocaluniformmeshesareused.

简介：ThispaperpresentsthedualbasesforanewfamilyofgeneralizedBallcurveswithapositionparameterK,whichincludestheBeziercurve,generalizedSaid-Ballcurveandsomeintermediatecurves.Usingthedualbases,therelativeMarsdenidentity,conversionformulasofbasesandcontrolpointsofvariouscurvesareobtained.

简介：Thepurposeofthispaperistostudythecascadicmultigridmethodforthesecondorderellipticproblemswithcurvedboundaryintwo-dimensionwhicharediscretizedbytheisoparametricfiniteelementmethodwithnumericalintegration.WeshowthattheCCGmethodisaccuratewithoptimalcomplexityandtraditionalmultigridsmoother(likesymmetricGauss-Seidel,SSORordampedJacobiiteration)isaccuratewithsuboptimalcomplexity.

简介：Inthispaper,theapplicationofhomotopymethodstotheloadflowmulti-solutionproblemsofpowersystemsisintroduced.BythegeneralizedBernshteintheorem,thecombinatorialnumberC2n^misshowntobetheBKKboundofthenumberofisolatedsolutionsofthepolynomialsystemtransformedfromloadflowequationswithgenericallychosencoefficients.AsaresultofthegeneralBezoutnumber,thenumberofpathsbeingfollowedisreducedsignificantlyinthepracticalloadflowcomputation.Finally,thecompleteP-Vcuresareobtainedbytrackingtheloadflowwithhomotopymethods.

简介：Inthisarticleweconsiderthefullydiscretetwo-levelfiniteelementGalerkinmethodforthetwo-dimensionalnonstationaryincompressibleNavier-Stokesequations.ThismethodconsistsindealingwiththefullydiscretenonlinearNavier-StokesproblemonacoarsemeshwithwidthHandthefullydiscretelineargeneralizedStokesproblemonafinemeshwithwidthh<

简介：Inthisarticleweconsideratwo-levelfiniteelementGalerkinmethodusingmixedfiniteelementsforthetwo-dimensionalnonstationaryincompressibleNavier-Stokesequations.ThemethodyieldsaH^1-optimalvelocityapproximationandaL^2-optimalpressureapproximation.Thetwo-levelfiniteelementGalerkinmethodinvolvessolvingonesmall,nonlinearNavier-StokesproblemonthecoarsemeshwithmeshsizeH,onelinearStokesproblemonthefinemeshwithmeshsizeh<

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.

简介：Inthispaper,wediscusstheconvergenceoftheBroydenalgorithmswithrevisedsearchdirection.Undersomeinexactlinesearches,weprovethatthealgorithmsaregloballyconvergentforcontinuouslydifferentiablefunctionsandtherateoflocalconvergenceofthealgorithmsisone-stepsuperlinearandn-stepsecond-orderforuniformlyconvexobjectivefunctions.

简介：Inthispapertheleast-squaresmixedfiniteelementisconsideredforsolvingsecondorderellipticproblemsintwodimensionaldomains.Theprimarysolutionuandthefluxerareapproximatedusingfiniteelementspacesconsistingofpiecewisepolynomialsofdegreekandrrespectively.Basedoninterpolationoperatorsandanauxiliaryprojection,superconvergentH^1-errorestimatesofboththeprimarysolutionapproximationuhandthefluxapproximationσhareobtainedunderthestandardquasi-uniformassumptiononfiniteelementpartition.ThesuperconvergenceindicatesanaccuracyofO(h^r+2)fortheleast-squaresmixedfiniteelementapproximationifRaviart-ThomasorBrezzi-DouglasFortin-MarinielementsoforderrareemployedwithoptimalerrorestimateofO(h^r+l).

简介：Iterativetechniquesforsolvingoptimalcontrolsystemsgovernedbyparabolicvariationalinequalitiesarepresented.Thetechniquesweusearebasedonlinearfiniteelementsmethodtoapproximatethestateequationsandnonlinearconjugategradientmethodstosolvethediscreteoptimalcontrolproblem.Convergenceresultsandnumericalexperimentsarepresented.

简介：Somenonlinearapproximants,i.e.,exponential-suminterpolationwithequaldistanceoratorigin,(0,1)-type,(0,2)-typeand(1,2)-typefraction-sumapproximations,formatrixvaluedfunctionsareintroduced.Alltheseapproximationproblemsleadtoasameformsystemofnonlinearequations.Solvingmethodsforthenonlinearsystemarediscussed.Conclusionsonuniquenessandconvergenceoftheapproximantsforcertainclassoffunctionsaregiven.

简介：Inthispaper,weinvestigatetheoptimalityconditionsofaclassofspecialnonsmoothprogrammingminF(x)=∑mi=1|max{fi(x),ci}|whicharisesfromLl-normoptimization,whereci∈Risconstantandfi∈C^l,i=1,2,…,m.Theseconditionscaneasilybetestedbycomputer.