Approximate solution of a singular integral equation using Chebyshev series

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Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system's guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	DOI: 10.23671/VNC.2016.4.5985 Approximate solution of a singular integral equation using Chebyshev series Besaeva Z. V. , Khubezhty Sh. S. Vladikavkaz Mathematical Journal 2016. Vol. 18. Issue 4. Abstract: A new method of approximate solution of singular integral equations with application of Chebyshev series is offered. Decomposition coefficients are determined by means of the solution of systems of simple algebraic equations. A justification of the constructed computational scheme is given and error estimate is deduced. The method is illustrated by test examples. Keywords: singular integral, Chebyshev series, approximation of integral, error estimation, orthogonal polynomial, coefficient of expansion. Language: Russian Download the full text + References 1. Lavrent'ev M. A. O postroenii potoka, obtekayushchego dugu zadannoj formy, Tr. CAGI [Trudy TsAGI], 1932, no. 118, pp. 3-56 2. Muskhelishvili N. I. Singulyarnye integral'nye uravneniya [Singular Integral Equations]. M.: Nauka, 1968. 512 p. [in Russian]. 3. Belotserkovsky S. M., and Lifanov I. K. Chislennye metody v singulyarnyh integral'nyh uravneniyah [Numerical Methods for Singular Integral Equations], Nauka, Moscow, 1985, 252 p. [in Russian]. 4. Lifanov I. K. Metod singulyarnykh integral'nykh ur avneniy i chislennyy eksperiment [Methods of singular integral equations and numerical experiments]. Moscow: Yanus, 1995, 520 p. 5. Paszkowski S. Vychislitel'nye primeneniya mnogochlenov i ryadov CHebysheva [Numerical Applications of Chebyshev Polynomials and Series], Nauka, Moscow, 1983, 384 p. [in Russian]. 6. Krylov V. I. Approximate Calculation of Integrals, The Macmillan Co., New York-London, 1962. 7. Khubezhty Sh. S. Kvadraturnye formuly dlya singulyarnyh integralov i nekotorye ih primeneniya [Quadrature Formulas for Singular Integrals and Some of Their Applications]. Vladikavkaz, 2011, 236 p. 8.Suetin P. K. Klassicheskie ortogonal'nye mnogochleny [Classical orthogonal polynomials] (Second ed.), 1979, Nauka, Moscow, 406 p. [in Russian]. 9. Natanson I. P. Konstruktivnaya teoriya funkcii [Constructive Function Theory], GIFML, Moscow, 688 p. [in Russian]. 10. Kantorovich L. V., Akilov G. P. Functional Analysis in Normed Spaces. The Macmillan Company, Publishers, New York, 1964. The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses. ← Contents of issue


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