Explicit finite difference schemes with extended stability for advection equations

In this study an explicit central difference approximation of the generalized leap-frog type is applied to the one- and two-dimensional advection equations. The stability of the considered numerical schemes is investigated and the scheme with the largest stable time step is found. For the linear and nonlinear advection equations numerical experiments with different schemes from the considered class are performed in order to evaluate the practical stability of the designed schemes.