简介:ThispaperisconcernedwithnumericalmethodsforAmericanoptionpricing.Weemploynumericalanalysisandthenotionofviscositysolutiontoshowuniformconvergenceoftheexplicitdifferenceschemeandthebinomialtreemethod.Wealsoprovetheexistenceandconvergenceoftheoptimalexerciseboundariesintheaboveapproximn.tions.
简介:Theinitial-boundaryvalueproblemofBurgersequationisconsidered.Aprediction-correctionLegendrespectralschemeisproposed.Itpossessestheaccuracyofsecondorderintimeandhigherorderinspace.Thenumericalexperimentsshowthehighaccuracyofthisapproach.
简介:Weproposeaschemeforteleportationoffour-levelatomicstatesinthermalcavities.TheschemedoesnotinvolvethegeneralizedBell-stateorgeneralizedGHZ-statemeasurement,whichisdifficultinpractice.Anotherfeatureoftheschemeisthatitdoesnotrequireindividualaddressingofatomsincavityandisinsensitivetobothcavitydecayandthermalfield,whichisofimportanceinpointofexperiment.
简介:Designofenergeticmaterialsisanexcitingareainmechanicsandmaterialsscience.Energeticcompositematerialsareusedaspropellants,explosives,andfuelcellcomponents.Energyreleaseinthesematerialsareaccompaniedbyextremeevents:shockwavestravelattypicalspeedsofseveralthousandmeterspersecondandthepeakpressurescanreachhundredsofgigapascals.Inthispaper,wedevelopareactivedynamicscodeformodelingdetonationwavefeaturesinonesuchmaterial.Thekeycontributioninthispaperisanintegratedalgorithmtoincorporateequationsofstate,Arrheniuskinetics,andmixingrulesforparticledetonationinaTaylor–Galerkinfiniteelementsimulation.Weshowthattheschemecapturesthedistinctfeaturesofdetonationwaves,andthedetonationvelocitycompareswellwithexperimentsreportedinliterature.
简介:TheHamiltonianformulationsofthelinear'good'Boussinesq(L.G.B.)equationandthemulti-symplecticformulationofthenonlinear'good'Boussinesq(N.G.B.)equationareconsidered.Forthemulti-symplecticformulation,anewfifteen-pointdifferenceschemewhichisequivalenttothemulti-symplecticPreissmannintegratorisderived.Wealsopresentnumericalexperiments,whichshowthatthesymplecticandmultisymplecticschemeshaveexcellentlong-timenumericalbehavior.
简介:Anewalternatingdirection(AD)finiteelement(FE)schemefor3-dimensionalnonlinearparabolicequationandparabolicintegro-differentialequationisstudied.ByusingAD,the3-dimensionalproblemisreducedtoafamilyofsinglespacevariableproblems,calculationworkissimplified;byusingFE,highaccuracyiskept;byusingvarioustechniquesforprioriestimatefordifferentialequationssuchasinductivehypothesisreasoning,thedifficultyarisingfromthenonlinearityistreated.ForbothFEandADFEschemes,theconvergencepropertiesarerigorouslydemonstrated,theoptimalH1-andL2-normspaceestimatesandtheO((△t)2)estimatefortimevariableareobtained.
简介:TheuseoftheLaserMegaJoulefacilitywithintheshockignitionschemehasbeenconsidered.Inthefirstpartofthestudy,one-dimensionalhydrodynamiccalculationswereperformedforaninertialconfinementfusioncapsuleinthecontextoftheshockignitionschemeprovidingtheenergygainandanestimationoftheincreaseofthepeakpowerduetothereductionofthephotonpenetrationexpectedduringthehigh-intensityspikepulse.Inthesecondpart,weconsideredaLaserMegaJouleconfigurationconsistingof176laserbeamsthathavebeengroupedprovidingtwodifferentirradiationschemes.Inthisconfigurationthemaximumavailableenergyandpowerare1.3MJand440TW.Optimizationofthelaser–capsuleparametersthatminimizetheirradiationnon-uniformityduringthefirstfewnsofthefootpulsehasbeenperformed.ThecalculationstakeintoaccountthespecificellipticallaserintensityprofileprovidedattheLaserMegaJouleandtheexpectedbeamuncertainties.Asignificantimprovementoftheilluminationuniformityprovidedbythepolardirectdrivetechniquehasbeendemonstrated.Three-dimensionalhydrodynamiccalculationshavebeenperformedinordertoanalysethemagnitudeoftheazimuthalcomponentoftheirradiationthatisneglectedintwodimensionalhydrodynamicsimulations.
简介:AFourierspectralschemeisproposedforsolvingtheperiodicproblemofnonlinearKlein-Gordonequation.Itsstabilityandconvergenceareinvestigated.Numericalresultsarealsopresented.
简介:Thispaperconsiderstheone-dimensionaldissipativecubicnonlinearSchrdingerequationwithzeroDirichletboundaryconditionsonaboundeddomain.Theequationisdiscretizedintimebyalinearimplicitthree-levelcentraldifferencescheme,whichhasanalogousdiscreteconservationlawsofchargeandenergy.Theconvergencewithtwoordersandthestabilityoftheschemeareanalysedusingaprioriestimates.Numericaltestsshowthatthethree-levelschemeismoreefficient.