APPROXIMATION OF FUNCTIONAL-ALGEBRAIC EIGENVALUE PROBLEMS

Abstract

A new symmetric variational functional-algebraic formulation of the eigenvalue problem in the Hilbert space with linear dependence on the spectral parameter for a class of mathematical models of thin-walled structures with an attached oscillator is proposed. The existence of eigenvalues and eigenvectors is established. A new symmetric approximation of the problem in a finite-dimensional subspace with linear dependence on the spectral parameter is constructed. Error estimates of the approximate eigenvalues and eigenvectors are obtained. The theoretical results are illustrated on the example of the problem of structural mechanics.