On reflected waves in the solutions of difference problems for the wave equation on non-uniform meshes

The paper discusses the problem of numerical reflected waves when using difference schemes on strongly nonuniform grids for solution to the wave equation. The relationship between the amplitude of the reflected wave and the order of approximation on the interface of the transition from a coarse grid to a fine grid is shown. A simple modification of the difference scheme on the interface is proposed, which increases the order of approximation, and, as a consequence, reduces the amplitude of the reflected wave.