Inthispaper,ahigh-orderfinite-volumeschemeispresentedfortheone-dimensionalscalarandinviscidEulerconservationlaws.TheSimpson’squadratureruleisusedtoachievehigh-orderaccuracyintime.TogetthepointvalueoftheSimpson’squadrature,thecharacteristictheoryisusedtoobtainthepositionsofthegridpointsateachsub-timestagealongthecharacteristiccurves,andthethird-orderandfifth-ordercentralweightedessentiallynon-oscillatory(CWENO)reconstructionisadoptedtoestimatethecellpointvalues.Severalstandardone-dimensionalexamplesareusedtoverifythehigh-orderaccuracy,convergenceandcapabilityofcapturingshock.
