Applied Physics and Mathematics Annotation << Back Employment of the difference mathematical model for computing the field in layered media I.A. Konnikov A comparative analysis of methods of solving in the wave equation is carried out, the electromagnetic field in flat-layered media being an instance. The gist of the method of the equivalent propagation constant is set out as the method is characteristic of a fairly wide frequency band and a comparatively little computational capacity. It is shown that the method of the equivalent propagation constant enables to reduce solving in the wave equation to solving in the Laplace equation for the electric and magnetic potentials of the field. The considered methods of solving in the Laplace equation for flat-layered media are based upon the employment of the Weber-Lipchitz identity and the employment of properties of the θ-function, the aspects demanding further exploration are formulated. The precision of long-established techniques of computing Green’s function is reported to rise if the method of difference mathematical model is employed; the gist of the method is set out. Diverse ways of construction of this mathematical model are explored by means of a computational experiment which also enables to confirm a statement about dependence of the error of computing Green’s function on the local inaccuracy of approximation of the flat-layered medium’s mathematical model. The hypothesis about the validity of the obtained results all over the domain of correct employment of the method of the equivalent propagation constant is founded heuristically. Кey words: Green function, Laplace equation, wave equation, equivalent propagation constant. Contacts: E-mail: konnikov_i@mail.ru Pp. 39-50.