caa a22 4500 378936417 CHVBK 20180305123641.0 cr unu---uuuuu 161128s2004 xx s 000 0 eng 10.2478/cmam-2004-0018 doi (NATIONALLICENCE)gruyter-10.2478/cmam-2004-0018 Functional-Discrete Method with a High Order of Accuracy for the Eigenvalue Transmission Problem [Elektronische Daten] We develop a functional-discrete method with a high order of accuracy to find a numerical solution of an eigenvalue transmission problem. It allows to approximate the trial eigenvalue with any desired accuracy. This approach has no restriction on the number of eigenvalues, an approximation to which can be found. The convergence rate is proved as in the case of the geometric series. It is shown that depending on the data of the original problem, two kinds of eigenvalue sequences may exist. For the first one, the convergence rate increases as the ordinal number of the trial eigenvalue increases. For the second one, the convergence rate is the same for all eigenvalues and does not depend on the ordinal number of the trial eigenvalue. Based on the asymptotic behavior of the eigenvalues of the basic problem and the functional-discrete method, a qualitative result on the arrangement of eigenvalues of the original problem is established. A number of numerical examples are given to support the theory. This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. eigenvalue transmission problem nationallicence functional-discrete method nationallicence basic problem nationallicence convergence rate like geometric series nationallicence Bessel functions nationallicence Makarov V.L. Institute of Mathematics, National Academy of Sciences of Ukraine, Tereschenkivska str. 3, 01601 Kyiv, Ukraine. Rossokhata N.O. Institute of Mathematics, National Academy of Sciences of Ukraine, Tereschenkivska str. 3, 01601 Kyiv, Ukraine. Bandurskii B.I. State University "L'vivs'ka Polytechnika", S.Bandera str. 5, 79013 L'viv, Ukraine. Computational Methods in Applied Mathematics De Gruyter 4/3(2004), 324-349 1609-4840 4:3<324 2004 4 cmam https://doi.org/10.2478/cmam-2004-0018 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.2478/cmam-2004-0018 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Makarov V.L. Institute of Mathematics, National Academy of Sciences of Ukraine, Tereschenkivska str. 3, 01601 Kyiv, Ukraine NATIONALLICENCE 700 1- Rossokhata N.O. Institute of Mathematics, National Academy of Sciences of Ukraine, Tereschenkivska str. 3, 01601 Kyiv, Ukraine NATIONALLICENCE 700 1- Bandurskii B.I. State University "L'vivs'ka Polytechnika", S.Bandera str. 5, 79013 L'viv, Ukraine NATIONALLICENCE 773 0- Computational Methods in Applied Mathematics De Gruyter 4/3(2004), 324-349 1609-4840 4:3<324 2004 4 cmam CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter