About implementation of boundary conditions in the bicompact schemes for a linear transport equation

The question of the boundary conditions implementation in the previously proposed bicompact schemes is investigated for the linear transfer equation. These schemes are constructed by the method of lines, they are conservative, monotonic and economical, and can be solved by running method. To ensure a high accuracy of the bicompact schemes, the various ways of implementing boundary conditions are proposed. These schemes are based on the $A$-and $L$-stable diagonally implicit Runge–Kutta of third-order approximation for the integration of the transfer equation in time.