On the convergence of Galerkin method for solving hypersingular integral equations in special classes of functions
- 作者: Smirnov Y.G.1
-
隶属关系:
- Penza State University
- 期: 编号 3 (2025)
- 页面: 3-12
- 栏目: MATHEMATICS
- URL: https://journals.rcsi.science/2072-3040/article/view/360874
- DOI: https://doi.org/10.21685/2072-3040-2025-3-1
- ID: 360874
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Background. The numerical method for solving hypersingular integral equations on a segment that arise in many problems of mathematical physics is considered. Materials and methods. Galerkin method is used to solve hypersingular equations with basic functions – Chebyshev polynomials of the 2nd kind. The projection method is considered in special classes of functions. Results and conclusions. The convergence of Galerkin method for solving hypersyngular equations in special classes of functions is proved. An estimate of the convergence rate of Galerkin method is obtained.
作者简介
Yuriy Smirnov
Penza State University
编辑信件的主要联系方式.
Email: mmm@pnzgu.ru
Doctor of physical and mathematical sciences, professor, head of the sub-department of mathematics and supercomputer modeling,
(40 Krasnaya street, Penza, Russia)参考
- Ilyinsky A.S., Smirnov Yu.G. Electromagnetic Wave Diffraction by Conducting Screens. VSP, Utrecht, the Netherlands, 1998:114.
- Shestopalov Yu.V., Smirnov Yu.G., Chernokozhin E.V. Logarithmic Integral Equations in Electromagnetics. VSP, Utrecht, the Netherlands, 2000:117.
- Lifanov I.K., Poltavskii L.N., Vainikko M.M. Hypersingular Integral Equations and Their Applications. 1st ed. CRC Press, 2003:396.
- Setukha A.V. Metod integralnykh uravneniy v matematicheskoy fizike: ucheb. posobiye = Method of integral equations in mathematical physics: textbook. Moscow: Izd-vo Mosk. un-ta, 2023:316. (In Russ.)
- Smirnov Yu.G. Matematicheskiye metody issledovaniya zadach elektrodinamiki = Mathematical methods for studying problems of electrodynamics. Penza: Inf.-izd. tsentr PenzGU, 2009:268. (In Russ.)
- Suyetin P.K. Klassicheskiye ortogonalnyye mnogochleny = Classical orthogonal polynomials. Moscow: Nauka, 1979:416. (In Russ.)
- Smirnov Yu.G. On the Fredholm property of hypersingular integral operators in special classes of functions. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fiziko- matematicheskiye nauki = University proceedings. Volga region. Physical and mathematical sciences. 2025;(2):3–14. (In Russ.). doi: 10.21685/2072-3040-2025-2-1
- Lyuk Yu. Spetsialnyye matematicheskiye funktsii i ikh approksimatsii = Special mathematical functions and their approximations. Moscow: Mir, 1980:608. (In Russ.)
- Smirnov Yu.G. Proyektsionnyye metody = Projection methods. Penza: Izd-vo PGTU, 1997. (In Russ.)
- Kress R. Linear Integral Equations. Applied Mathematical Sciences, 82. Springer- Verlag, New York, 1999:365.
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