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一类广义Zakharov方程组拟谱方法的整体误差估计(Ⅱ)(英文) Title:GlobalErrorEstimationfortheSpectralApproximationofaClassofGeneralizedZakharovEquationSystems(PartII) Abstract: Inthefirstpartofthispaper,weintroducedaspectralmethodforsolvingaclassofgeneralizedZakharovequationsystemsanddemonstrateditsconvergenceusingalocalerroranalysis.Inthissecondpart,wepresentaglobalerroranalysisthatprovidesanestimateforthesizeoftheerrorinthespectralapproximationovertheentirecomputationaldomain. ThegeneralizedZakharovequationsystemisamodelthatdescribesthebehaviorofweaklynonlinearwavesinadispersivemediumwithatwo-dimensionalwavevector.ThespectralmethodweuseinvolvesapproximatingthesolutionusingaseriesofFouriermodes.Whilethismethodiswidelyusedforsolvingpartialdifferentialequations,itrequiresacarefulanalysistoensureconvergenceandaccuracyofthesolution. Intheglobalerroranalysis,wefirstobtainadifferentialequationfortheerrorbysubtractingthetruesolutionfromthespectralapproximationandapplyingtheequationsystem.WethenusetheFouriertransformtoconvertthedifferentialequationtoanalgebraicequationfortheFouriercoefficientsoftheerror.Byanalyzingthepropertiesofthealgebraicequation,weobtainaboundfortheerrorintermsofthenormoftheinitialconditionandthenumberofFouriermodesusedintheapproximation. Wedemonstratetheeffectivenessofourmethodbyapplyingittoatestproblemwithknownsolution.Wecomparethecomputedsolutionwiththeexactsolutionandtheerrorestimatetodemonstratetheaccuracyofthemethod.OurresultsshowthatthespectralmethodisabletoaccuratelycapturethebehaviorofthegeneralizedZakharovequationsystemoverawiderangeofparameters. Insummary,thispaperprovidesaglobalerroranalysisforaspectralmethodthatcanbeappliedtoaclassofgeneralizedZakharovequationsystems.Theanalysisprovidesanestimateforthesizeoftheerrorinthespectralapproximationovertheentirecomputationaldomain.Themethodisdemonstratedtobeaccurateandeffectivethroughtheresultsofatestproblem.