Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111240
Title: Harmonic Interpolating Wavelets in the Neumann Boundary Value Problem in a Ring
Other Titles: Гармонические интерполяционные всплески в краевой задаче Неймана в кольце
Authors: Yamkovoi, D. A.
Issue Date: 2020
Publisher: Krasovskii Institute of Mathematics and Mechanics
Krasovskii Institute of Mathematics and Mechanics UB RAS
Citation: Yamkovoi D. A. Harmonic Interpolating Wavelets in the Neumann Boundary Value Problem in a Ring [Гармонические интерполяционные всплески в краевой задаче Неймана в кольце] / D. A. Yamkovoi // Trudy Instituta Matematiki i Mekhaniki UrO RAN. — 2020. — Vol. 26. — Iss. 4. — P. 279-289.
Abstract: We consider the Neumann boundary value problem with continuous boundary values in a centrally symmetric ring with unit outer radius. The approach to solving the problem is based on expanding the continuous boundary values in interpolating and interpolating orthogonal 2π-periodic wavelets consisting of trigonometric polynomials. The idea for such an expansion and the scheme of interpolating and interpolating orthogonal 2π-periodic wavelets based on Meyer-type wavelets were proposed by Yu.N. Subbotin and N.I. Chernykh. It is convenient to use these series due to the fact that they are easily extended to polynomials harmonic in a circle, and the harmonic polynomials can be used to present the solution of the original problem in a ring as two series uniformly convergent in the closure of the ring. Moreover, the coefficients of the series are easily calculated and do not require the calculation of integrals. As a result, we obtain an exact representation for the solution of the Neumann boundary value problem in the ring in the form of two series in the mentioned system of harmonic wavelets and find an estimate for the error of approximating the exact solution by partial sums of the series. © 2020 Krasovskii Institute of Mathematics and Mechanics. All rights reserved.
Keywords: HARMONIC FUNCTIONS
INTERPOLATING WAVELETS
NEUMANN BOUNDARY VALUE PROBLEM
URI: http://hdl.handle.net/10995/111240
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85103677613
PURE ID: 20231640
ISSN: 0134-4889
metadata.dc.description.sponsorship: This study is a part of the research carried out at the Ural Mathematical Center.
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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