Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)3301410.22363/2658-4670-2022-30-4-330-341Research ArticleOn a dispersion curve of a waveguide filled with inhomogeneous substanceKroytorOleg K.<p>Senior lecturer of Department of Applied Probability and Informatics</p>kroytor-ok@rudn.ruhttps://orcid.org/0000-0002-5691-7331MalykhMikhail D.<p>Doctor of Physical and Mathematical Sciences, Assistant Professor of Department of Applied Probability and Informatics</p>malykh-md@rudn.ruhttps://orcid.org/0000-0001-6541-6603Peoples’ Friendship University of Russia (RUDN University)Joint Institute for Nuclear Research2612202230433034126122022Copyright © 2022, Kroytor O.K., Malykh M.D.2022<p style="text-align: justify;">The paper discusses the relationship between the modes traveling along the axis of the waveguide and the standing modes of a cylindrical resonator, and shows how this relationship can be explored using the Sage computer algebra system. In this paper, we study this connection and, on its basis, describe a new method for constructing the dispersion curve of a waveguide with an optically inhomogeneous filling. The aim of our work was to find out what computer algebra systems can give when calculating the points of the waveguide dispersion curve. Our method for constructing the dispersion curve of a waveguide with optically inhomogeneous filling differs from those proposed earlier in that it reduces this problem to calculating the eigenvalues of a self-adjoint matrix, i.e., a well-studied problem. The use of a selfadjoint matrix eliminates the occurrence of artifacts associated with the appearance of a small imaginary addition to the eigenvalues. We have composed a program in the Sage computer algebra system that implements this method for a rectangular waveguide with rectangular inserts and tested it on SLE modes. 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