Compensation of the scheme dispersion and dissipation by artificial non-linear additions

It is known that dispersive/dissipative features of the difference schemes used for simulations may be described by their differential approximations (DA). It is shown, that exact traveling wave solutions of the DA for the nonlinear Burgers equation help us to suggest artificial additions to the schemes to suppress the influence of the scheme dispersion and dissipation. Analytical predictions are confirmed using modifications of some familiar schemes, namely, the Lax-Wendroff, Warming-Beam and the third-order Lax-Wendroff schemes.