Implicit-Explicit Bicompact Schemes for Hyperbolic Systems of Conservation Laws

High-order bicompact schemes for hyperbolic systems of conservation laws are considered. We aim to significantly speed up these schemes. Implicit-explicit Runge–Kutta methods are proposed for time discretization, instead of the previously used diagonally implicit methods. The global Lax–Friedrichs–Rusanov flux splitting is a premise for the implicit-explicit approximation. It is shown that implicit-explicit bicompact schemes are stable for any ratio of steps in time and space. The accuracy of the new implicit-explicit schemes and the substantial speed-up achieved are demonstrated on multidimensional gas dynamics problems.