1D and 2D bicompact schemes in layered mediums

New type of differential schemes – so called bicompact schemes was considered. To derive such schemes we transform PDE into system of PDEs. Spatial derivatives are approximated on 2-points stencil, i.e. within single grid step. In layered mediums bicompact schemes keep their approximation if we set a special grid in a way that all points where coefficients have breaks are nodes of the grid. Two schemes for 1-dimensional hyperbolic problem were considered in details and schemes for 2D problems are given.