Advanced Method for Solving the Non-linear Multiparameter Spectral Problems

Abstract

An effective numerical method for solving non-linear multiparametric spectral problems for the holomorphic operator-functions, which belong to the Banach spaces is proposed. The theorem of existence of connected components of the spectrum (CCS), the finding of which consists in solving a system of equations of partial derivatives of the first order with the corresponding initial condition, is proved. The examples of solving three-parameter spectral problems are given.