Modification of the Cabaret scheme ensuring its high accuracy on local extrema

It's shown that the standard flux correction which is necessary for monotonicity of the CABARET scheme leads to reduction of its accuracy near local extrema. Modified flux correction is proposed that ensures the strong monotonicity of the CABARET scheme for Courant numbers $r\in (0,0.5]$ and simultaneously preserves its high accuracy near local extrema. Test computations of discontinuous solutions of nonlinear advection equation are presented that illustrate advantages of modified scheme.