Physics of Wave Processes and Radio SystemsPhysics of Wave Processes and Radio Systems1810-31892782-294XPovolzhskiy State University of Telecommunications and Informatics980810.18469/1810-3189.2021.24.3.18-27Research ArticleThe method of simple iterations with correction of convergence and the minimal discrepancy method for plasmonic problemsDavidovichMikhail V.<p>Doctor of Physical and Mathematical Sciences, Professor of the Department of Radio Engineering and Electrodynamics </p>davidovichmv@info.sgu.ruKobetzAlexander K.<p>Quality Director </p>kobetzak@info.sgu.ruSayapinKirill A.<p>postgraduate student of the Department of Radio Engineering and Electrodynamics, Institute of Physics</p>sayapin_kirill@mail.ruSaratov State UniversityLLC «NPF “Etna plus”»18112021243182718112021Copyright © 2021, Davidovich M., Kobetz A., Sayapin K.2021<p>The problem of searching for complex roots of the dispersion equations of plasmon-polaritons along the boundaries of the layered structure-vacuum interface is considered. Such problems arise when determining proper waves along the interface of structures supporting surface and leakage waves, including plasmons and polaritons along metal, dielectric and other surfaces. For the numerical solution of the problem, we consider a modification of the method of simple iterations with a variable iteration parameter leading to a zero derivative of the right side of the equation at each step, i.e. convergent iterations, as well as a modification of the minimum residuals method. It is shown that the method of minimal residuals with linearization coincides with the method of simple iterations with the specified correction. Convergent methods of higher orders are considered. The results are demonstrated by examples, including complex solutions of dispersion equations for plasmon-polaritons. 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