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A large class of scattering and propagation problems can be reduced to a system of dual series equations. This system of equations can be rigorously solved in an efficient manner by the method based on the Riemann-Hilbert problem. Although the presence of an edge introduces some distinctive features, it was pointed out that the Riemann-Hilbert approach explicitly accounted for the singularity of the fields near the edge. In the present work, the dual series equations for a gyrotropic circular rod covered with metal strip are solved by the modified method for the Riemann-Hilbert problem.