Inthispaper,akindofexplicitdifferenceschemetosolvenonlinearevolutionequations,perfectlykeepingthesquareconservationbyadjustingthetimestepinterval,isconstructed,fromthecomprehensivemaintenanceofthead-vantagesoftheimplicitcompletesquareconservativeschemeandtheexplicitinstantaneoussquareconservativescheme.Thenewschemesarebasedonthethoughtofaddingasmalldissipation,butitisdifferentfromthesmalldissipationmethod.Thedissipativetermusedinthenewschemesisnotasimpleartificialdissipativeterm,butaso-called(time)harmoniousdissipativetermthatcancompensateforthetruncationerrorsfromthedissociationofthetimedifferentialterm.Therefore,thenewschemesmayhaveahightimeprecisionandmayacquireasatisfactoryeffectinnumericaltests.
