简介：ThispaperintroducesthedefinitionoftheOrthogonalTypeNodeConfigurationanddiscussesthecorrespondingmultivariateLagrange,HermiteandBirkhoffinterpolationproblemsinhighdimensionalspaceRs(s＞2).ThisnodeconfigurationcanbeconsideredtobeakindofextensionoftheCrossTypeNodeConfiguration[1],[2]inR2tohighdimensionalspaces.AndtheMixedTypeNodeConfigurationinRs(s＞2)isalsodiscussedinthispaperinanexample.

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简介：Mathergavethenecessaryandsufficientconditionsforthefinitedeterminacys-moothfunctiongermswithnomorethancodimension4.Thetheoremisveryeffectiveondetermininglowcodimensionsmoothfunctiongerms.Inthispaper,theconceptofrightequivalentforsmoothfunctiongermsringgeneratedbytwoidealsfinitelyisdefined.Thecontainmentrelationshipsoffunctiongermsstillsatisfyfinitek-determinacyundersufficientlysmalldisturbancewhicharediscussedinorbittangentspaces.Furthermore,themethodsinjudgingtherightequivalencyofArnoldfunctionfamilywithcodimension5arepresented.

简介：Split-stepPadémethodandsplit-stepfouriermethodareappliedtothehigher-ordernonlinearSchrdingerequation.ItisprovedthatacombinationofPadéschemeandspectralmethodisthemosteffectivemethod,whichhasaspectral-likeresolutionandgoodstabilitynature.Inparticular,weproposeanunconditionalstableimplicitPadéschemetosolveoddordernonlinearequations.NumericalresultsdemonstratetheexcellentperformanceofPadéschemesforhighordernonlinearequations.

简介：TheBesovspacesBpα,4（Γ）andTriebel-LizorkinspacesFpα,4（Γ）withhighorderx∈RonaLipschitzcurveΓaredefind,when1≤p≤∞,1≤q≤∞.Tocomparetotheclassicalcase.adifferencecharacterizationofsuchspacesinthecase|x|<1isgivenalso.

简介：Abstract.Usingthemethodofundeterminedfunction,asetof12parameterrectangularp|atedementwithdoub[esetparameterandgeometrysymmetryisconstructed.TheirconsistencyerrorareO(h2),oneorderhigherthantheusua[12parameterrectangu|arp[ateelements.

简介：AbstractInthispaperwestudysomenonoverlappingdomaindecompositionmethodsforsolvingaclassofellipticproblemsarisingfromcompositematerialsandflowsinporousmediawhichcontainmanyspatialscales.Ourpreconditionerdiffersfromtraditionaldomaindecompositionpreconditionersbyusingacoarsesolverwhichisadaptivetosmallscaleheterogeneousfeatures.Whiletheconvergencerateoftraditionaldomaindecompositionalgorithmsusingcoarsesolversbasedonlinearorpolynomialinterpolationsmaydeteriorateinthepresenceofrapidsmallscaleoscillationsorhighaspectratios,ourpreconditionerisapplicabletomultiple-scaleproblemswithoutrestrictiveassumptionsandseemstohaveaconvergenceratenearlyindependentoftheaspectratiowithinthesubstructures.ArigorousconvergenceanalysisbasedontheSchwarzframeworkiscarriedout,andwedemonstratetheefficiencyandrobustnessoftheproposedpreconditionerthroughnumericalexperimentswhichincludeproblemswithmultipl

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简介：ErrorestimatesofGalerkinmethodforKuramoto-Sivashingsky(K-S)equationinspacedimension≥3arederivedinthepaper.Theseresultsfurnishstrongevidenceforthecom-putationofthesolutions.

简介：Inthispaper,analmostP-stabletwo-stepsixth-orderHybridmethodwithphase-lagoforderinfinityandaclassexpliciteighth-orderObreckoffmethodswithphase-lagoforder10-24aredevelopedforthenumericalintegrationofthespecialsecond-orderperiodicinitial-valueproblems.Thesemethodshavetheadvantageofhigheralgebraicorderandconsiderablysmallerphase-tagcomparedwithsomemethodsin[1-6].Numericalexamplesindicatethatthesenewmethodsaremoreaccuratethanmethodsdevelopedby[1-6].

简介：Thispaperintroducestheuseofpartitionofunitymethodforthedevelopmentofahighorderfinitevolumediscretizationschemeonunstructuredgridsforsolvingdiffusionmodelsbasedonpartialdifferentialequations.Theunknownfunctionanditsgradientcanbeaccuratelyreconstructedusinghighorderoptimalrecoverybasedonradialbasisfunctions.Themethodologyproposedisappliedtothenoiseremovalprobleminfunctionalsurfacesandimages.Numericalresultsdemonstratetheeffectivenessofthenewnumericalapproachandprovideexperimentalorderofconvergence.

简介：Westudypreconditioningtechniquesusedinconjunctionwiththeconjugategradientmethodforsolvingmulti-length-scalesymmetricpositivedefinitelinearsystemsoriginatingfromthequantumMonteCarlosimulationofelectroninteractionofcorrelatedmaterials.Existingpreconditioningtechniquesarenotdesignedtobeadaptivetovaryingnumericalpropertiesofthemulti-length-scalesystems.Inthispaper,weproposeahybridincompleteCholesky(HIC)preconditioneranddemonstrateitsadaptivitytothemulti-length-scalesystems.Inaddition,weproposeanextensionofthecompressedsparsecolumnwithrowaccess(CSCR)sparsematrixstorageformattoefficientlyaccommodatethedataaccesspatterntocomputetheHICpreconditioner.Weshowthatformoderatelycorrelatedmaterials,theHICpreconditionerachievestheoptimallinearscalingofthesimulation.Thedevelopmentofalinear-scalingpreconditionerforstronglycorrelatedmaterialsremainsanopentopic.

简介：Inthispaper,ahighaccuracyfinitevolumeelementmethodispresentedfortwo-pointboundaryvalueproblemofsecondorderordinarydifferentialequation,whichdiffersfromthehighordergeneralizeddifferencemethods.Itisprovedthatthemethodhasoptimalorderer-rorestimateO(h3)inH1norm.Finally,twoexamplesshowthatthemethodiseffective.

简介：Ahigh-orderleap-frogbasednon-dissipativediscontinuousGalerkintime-domainmethodforsolvingMaxwell'sequationsisintroducedandanalyzed.Theproposedmethodcombinesacenteredapproximationfortheevaluationoffluxesattheinterfacebetweenneighboringelements,withaNth-orderleap-frogtimescheme.Moreover,theinterpolationdegreeisdefinedattheelementlevelandthemeshisrefinedlocallyinanon-conformingwayresultinginarbitrarylevelhangingnodes.ThemethodisprovedtobestableundersomeCFL-likeconditiononthetimestep.Theconvergenceofthesemi-discreteapproximationtoMaxwell'sequationsisestablishedrigorouslyandboundsontheglobaldivergenceerrorareprovided.Numericalexperimentswithhigh-orderelementsshowthepotentialofthemethod.