Comparison of methods for solving the diffraction problem for a step in a waveguide

Using the example of wave diffraction at a step in a circular waveguide, different methods of solving the problem, based on matching of the fields, are compared. It is show that the problem can be reduced to two different infinite sets of algebraic equations. Jouns' method, the method of scattering matrices, and the method of regularization, lead to one system. The other is obtained from the matching method and the generalized matching method. Organization of the computational process to obtain the matrix of the second system is simpler and faster.