Improvement of the monotonicity properties of the difference schemes by   building in them of the monotonizing operators
  The method of monotonization of difference schemes is being considered in the paper. The method was earlier proposed by the author for stationary problems. It is investigated in the paper more profoundly. The idea of the method is to build the monotonizing operators into the schemes so that the balance relations from point to point are not violated. Different monotonizing operators can be used to be installed in the schemes. Propositions concerning approximation and stability of the monotonized schemes are formulated and proved. Also a proposition significant for practical use of the schemes is formulated and proved. The idea is to use the monotonized schemes in the cases when the proposition conditions are fulfilled. The proposition is based on closeness of solutions of the initial and auxiliary schemes. Constructions for solving of time dependent problems are also written in the paper. One dimensional example and three-dimensional hydrodynamic example are considered. The method allows to considerably decrease value of calculations in many cases. 
Y. V. Troshchiev
cs.NA math.NA