NUMERICAL INVESTIGATION OF THE INVERSE PROBLEM FOR THE BOUSSINESQ -- LOVE MATHEMATICAL MODEL ON A GRAPH

Abstract

The article is devoted to a numerical study of the Boussinesq -- Love mathematical model considered on a graph. The model under study describes longitudinal vibrations in a construction consisting of thin, elastic rods, taking into account the external load acting on them. To find the solution, the method of successive approximations is used, and the model itself is reduced to an incomplete second-order Sobolev type equation. The first paragraph contains the results on an analytical study of the model. In the second section, the developed algorithm of the numerical method and its scheme are presented. The third section presents the results of computational experiments obtained using the program developed in the Maple environment based on the developed algorithm. All the obtained results can be applied in the field of mathematical modeling, for example, when calculating the longitudinal vibrations in a construction, taking into account the external load acting on it.