ABSTRACT
In this chapter, we consider vibrations of an inhomogeneous system described by hyperbolic equations with the Dirichlet boundary conditions. It is assumed that the corresponding eigenvalue problem in a rectangular domain admits partial separation of the variables and the separation parameters enter both equations. Thus, we obtain a system with two parameters whose eigenvalues are to be determined jointly. For this purpose, we develop a method of accelerated convergence, which allows us to calculate approximations of any given order for eigenvalues and eigenfunctions of the problem with variable coefficients.
