Algorithms for calculating the eigenvalues of initial-boundary value problems for a wave differential equation set in a graph with varying edges

The paper develops algorithms for calculating the eigenvalues of initial-boundary value problems for a wave differential equation set in a star graph with time-varying edge lengths. The change of variables helped to reduce the considered spectral problems to initial-boundary value problems with fixed edges. The obtained formulas were used to find eigenvalues for a wave differential equation set in a star graph with time-varying edges with any ordinal numbers. The formulas for calculating the eigenvalues will allow developing algorithms for solving inverse spectral problems set in quantum graphs with varying edges.