On one class of high-order compact grid-characteristic schemes for linear advection

A class of two-point compact difference schemes of the second-third orders of accuracy on a twopoint coordinate stencil is considered for a one-dimensional transfer equation. All difference schemes are based on interpolation polynomials constructed on a given stencil. Based on the behaviour of the solution and the character of interpolation polynomials, we propose hybrid compact difference schemes of 2-3rd orders of accuracy on smooth functions producing solutions weakly smoothing the front of discontinuities. The study of grid convergence for the constructed difference scheme is carried out and the propagation of a pulse of complex form is simulated numerically for studying the behaviour of the difference scheme on discontinuous solutions.