2025 , Volume 30, № 4, p.119-132

The author dedicates this paper to Academician Yurii Ivanovich Shokin who over the past fifty five years has developed the theory of the modified partial differential equation (MDE) for the constant-wind-speed advection equation, advection-diffusion equation and for scalar hyperbolic conservation laws. Shokin, Yanenko and Vorozhtsov present a very precise approach to this problem. These scientists call the modified partial differential equation: Γ- and Π-form of the first differential approximation or Γ- and Π-form of the differential representation of the difference scheme. In the case of hyperbolic equations, the Π-form indicates the value of the Courant number of the separated dissipative or dispersive difference schemes. It also leads to the definition criterion of the stability of the difference method. In the monograph Shokin, Yanenko and Vorozhtsov stability criteria and examples of the abbreviated forms of MDE difference schemes, most popular in the mid-1980s are presernted in the tabular form