Expansion in eigenfunctions of the Sturm-Liouville problem on a bundle graph

In this paper we consider the applicability of the Fourier method for partial differential equations on spatial grids (we choose a bundle graph as a model). This leads to an important problem, namely, to the expansion of a given function in eigenfunctions of the corresponding Sturm-Liouville problem on a grid. We study a model problem which describes a symmetric case, when one considers physically identical one-dimensional continuums on the bundle graph. Such problems arise, for example, in the modeling of oscillating processes of an elastic mast with supporting elastic ties.