Upwind bicompact schemes for hyperbolic conservation laws

For the first time, upwind bicompact schemes of third order approximation in space are presented. A formula is obtained for the transition factor of an arbitrary fully discrete bicompact scheme with integration in time by a Runge–Kutta method. Stability and monotonicity of the first-order in time scheme are investigated, dissipative and dispersion properties of the third-order in time scheme are analyzed. Advantages of the new schemes relative to their centered counterparts are demonstrated.