Aclassofthree-levelexplicitdifferenceschemesforthedispersiveequationu1=auxxxareestablishedTheseschemeshavehigherstabilityandinvolvefourmeshpointsatthemiddlelevel.TheirlocaltruncationerrorsareO(τ+h)andstabilityconditionsarefrom|R|≤0.25to|R|≤10,where|R|=|a|τ/h3,whichismuchbetterthan|R|≤0.25.