Approximation of the solution of an internal problem of electrodynamics by the method of eigenfunctions

The problem of constructing approximation models of radiating and reradiating structures based on the eigenfunction method is considered. The ambiguity of the solution of this problem is noticed. Techniques are proposed which can be used in developing approximation models. An expression is presented for estimating the error introduced by the approximation model. As an example, one of the possible options for constructing an approximation model for a tubular antenna is given. The results of numerical simulation are presented.