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The study of the solvability of\nthis problem is based on the spectral theory of compact self-adjoint operators.\nProperties of dispersion curves are investigated for the new formulation of the problem.\nAn efficient numerical method based on FEM approximations is developed. Error estimates\nfor approximate solutions are derived. The rate of convergence for the presented\nalgorithm is investigated numerically.<\/jats:p>","DOI":"10.1515\/cmam-2017-0049","type":"journal-article","created":{"date-parts":[[2017,11,17]],"date-time":"2017-11-17T17:16:14Z","timestamp":1510938974000},"page":"581-601","source":"Crossref","is-referenced-by-count":7,"title":["Numerical Modeling of Optical Fibers Using the Finite Element\nMethod and an Exact Non-reflecting Boundary Condition"],"prefix":"10.1515","volume":"18","author":[{"given":"Rafail Z.","family":"Dautov","sequence":"first","affiliation":[{"name":"Department of Numerical Mathematics , Kazan Federal University , 18 Kremliovskaya street , Kazan 42008 , Russia"}]},{"given":"Evgenii M.","family":"Karchevskii","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics , Kazan Federal University , 18 Kremliovskaya street , Kazan 42008 , Russia"}]}],"member":"374","published-online":{"date-parts":[[2017,11,17]]},"reference":[{"key":"2026011715120268125_j_cmam-2017-0049_ref_001_w2aab3b7e2108b1b6b1ab2b1b1Aa","doi-asserted-by":"crossref","unstructured":"M.  Abramowitz and I. A.  Stegun,\nHandbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables,\nNatl. Bureau Standards Appl. Math. Ser. 55,\nU.S. Government Printing Office, Washington, 1964.","DOI":"10.1115\/1.3625776"},{"key":"2026011715120268125_j_cmam-2017-0049_ref_002_w2aab3b7e2108b1b6b1ab2b1b2Aa","doi-asserted-by":"crossref","unstructured":"S.  Acosta, V.  Villamizar and B.  Malone,\nThe DtN nonreflecting boundary condition for multiple scattering problems in the half-plane,\nComput. Methods Appl. Mech. Engrg. 217\/220 (2012), 1\u201311.","DOI":"10.1016\/j.cma.2012.01.005"},{"key":"2026011715120268125_j_cmam-2017-0049_ref_003_w2aab3b7e2108b1b6b1ab2b1b3Aa","doi-asserted-by":"crossref","unstructured":"A.  Bamberger and A. S.  Bonnet,\nMathematical analysis of the guided modes of an optical fiber,\nSIAM J. Math. 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