Nonlinear monotonization of K. I. Babenko scheme for the numerical solution of the quasi-linear advection equation

The paper is dedicated to testing the authors offered variant of nonlinear monotonised К. I. Babenko scheme for numerical solution of quasi-linear advection equation, as well as its comparison with other well-known finite-difference schemes. There were used for the comparison the implicit and explicit schemes with the left difference of first-order approximations, the Lax–Wendroff scheme of second order approximations, as well as monotonised ‘Cabaret’ scheme. The presented information about the errors of numerical solutions allows to compare a quality of the schemes. Benchmark analysis of the errors has shown that the offered scheme gives higher accuracy in the broad range of Courant numbers, as well as smaller 'smudging' decision of shocks.