On difference schemes with artificial dispersion

The interior dissipative and dispersion properties of difference schemes for non-linear hyperbolic equations are studied by analyzing the differential approximation. The examples of the quasilinear transport equation and the system of equations of isothermal gas dynamics are considered. A class of schemes with artificial dispersion is studied, whereby the distorting effect of interior dispersion and dissipation on the difference solution is weakened. The theoretical results are confirmed by direct computations.