The problem of electromagnetic wave transmission in a circular waveguide

The article deals with the problem of transmission in a circular waveguide, in the cross section of which there is a thin metal screen. The waveguide is bounded by a perfectly conducting surface. The transmission problem is an auxiliary problem that arose when solving inverse diffraction problems. In the transmission problem, it is required to find the electromagnetic field in the waveguide on one side of the screen by a given field on the other side of the screen: both by given waves incident on the screen and by given waves leaving the screen to infinity. It is shown how the transmission problem can be reduced to an infinite system of linear algebraic equations. To solve the resulting system, it is proposed to use the truncation method. We study under what conditions the numerical solution of the transmission problem will be stable to small perturbations of the input data.