Implicit-explicit bicompact schemes for hyperbolic systems of conservation laws

High-order bicompact schemes for hyperbolic systems of conservation laws are considered. The goal is to achieve a significant speed-up for 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 high accuracy of the new implicit-explicit schemes and the substantial speed-up are demonstrated on multidimensional gas dynamics problems.