About one choice of essentially non-oscillatory high occuracy order difference scheme for systems of conservation laws

Version of essentially non-oscillatory high occuracy order difference scheme for systems of conservation laws, based on minimization for norm of interpolation polynomial deviation from the cell averages was suggested in this paper. Such choice can give more monotonous solution in comparision with traditional ENO and WENO schemes of corresponding occuracy order, that was confirmed by results of numerical calculation for model problems.