NUMERICAL INVESTIGATION OF THE INITAL-FINAL PROBLEM FOR THE BOUSSINESQ -- LOVE EQUATION ON A GEOMETRICAL GRAPH

Abstract

The article is devoted to the analytical and numerical study of the initial-final problem for the Boussinesq -- Love equation describing longitudinal oscillations in a thin elastic rod. The solution of the problem is understood as a function that defines the longitudinal diaplacement in the components of the rod structure. To find it, the Fourier method is used. The first section presents a formal analytical solution to the problem. In the second section, the theorem on the existence of the solution and its uniqueness is proved. The third section describes an algorithm for finding approximate solution to the initial-final problem for the Boussinesq -- Love equation defined on graph. In the fourth section, a computational experiment is performed for the graph consisted of two edges.