Comparison of some numerical methods solutions of wave equations with strong dispersion

In this paper, four different difference schemes for solving boundary value problems for an equation with strong dispersion based on the finite difference method and the finite element method are proposed and studied. In spatial approximation of the problem, we considered schemes of various accuracy orders, from two to four. For the abstract Cauchy problem obtained by spatial approximation three parameter difference schemes of the fourth order precision finite element method are considered. The schemes are tested using a computational experiment. Their comparative analysis is carried out.