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The propagation of monochromatic electromagnetic waves in metal circular cylindrical dielectric waveguide with longitudinal magnetization filled with anisotropic inhomogeneous waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. Numerical results are obtained using a modification of the projecting methods. The comparison with known exact solutions (for particular values of parameters) are made.
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