Steady discrete shocks of high-order RBC schemes

Exact expressions of steady discrete shocks are found for a class of dissipative compact schemes approximating a one-dimensional nonlinear hyperbolic problem with a 3rd, 5th and 7th order of accuracy. A discrete solution is given explicitly for the inviscid Bürgers equation and the oscillatory nature of the shock profiles is determined according to the scheme order and to the shock location with respect to the mesh.