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