Natural oscillations of multidimensional systems nonlinear in the spectral parameter

Abstract

A new method of solving the generalized vector self-conjugated Sturm-Liouville boundary value problems with the boundary conditions of the first kind is proposed and developed. The iterative algorithm is based on a constructive procedure of introduction of a small parameter and an efficient correction of the desired eigenvalue. The matrix coefficients of the equations are assumed to be nonlinearly dependent on the spectral parameter. The criterion of proximity is introduced, and it is shown that this method has an accelerated convergence of the second order with respect to a small parameter for a reasonably close initial approximation. Test examples are considered.