Mathematical Modelling of Finding the Values of Eigenfunctions for the Electrical Oscillations in the Extended Line Problem Using the Method of Regularized Traces

Abstract

This paper describes a new numerical method for computing the values of the
eigenfunctions of perturbed self-adjoint operators. The new method is based on the
method of regularized traces. A mathematical model for calculating the eigenfunction
values of the spectral problem concerning electrical oscillations in the extended line is
developed. The elaborated algorithms make it possible to calculate the values of the
eigenfunction of the perturbed operator whether the previous values are known or not.
We’ve obtained the estimates of functional series residual sum¿suspendedÀ the corrections
of the perturbation theory of perturbed self-adjoint operators, and proved their convergence.
Effective algorithms for finding¿suspendedÀ perturbation theory corrections are discovered
for the numerical implementation of the method. The numerical experiments on the
calculation of the values of a problem on its own electrical oscillations in the extended lines
show that the method is consistent with the other well-known methods of A.N.Krylov and
A.M.Danilevsky. The method of regularized traces proved its reliability and high efficiency.