Numerical investigation of compact grid-characteristic schemes for acoustic problems

In this paper, an acoustic approximation is considered, which allows to describe the propagation of longitudinal waves in geological media. For the two-dimensional case, a compact numerical scheme is described that provides an increased approximation order on a two-point spatial stencil. To construct it, we used the method of splitting along coordinate axes and the differential continuation of the original system of equations. A number of numerical tests have been carried out, confirming the increased order of approximation.