Geodesic
Approximate solution of a singular integral equation using Chebyshev series
Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 4, pp. 15-22 
Z. V. Besaeva; Sh. S. Khubezhty. Approximate solution of a singular integral equation using Chebyshev series. Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 4, pp. 15-22. http://geodesic.mathdoc.fr/item/VMJ_2016_18_4_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Lavrentev M. A., “O postroenii potoka, obtekayuschego dugu zadannoi formy”, Tr. TsAGI, 118, 1932, 3–56

[2] Muskhelishvili N. I., Singulyarnye integralnye uravneniya, Nauka, M., 1968, 511 pp.

[3] Belotserkovskii S. M., Lifanov I. K., Chislennye metody v singulyarnykh integralnykh uravneniyakh, Nauka, M., 1985, 252 pp. | MR

[4] Lifanov I. K., Metod singulyarnykh integralnykh uravnenii i chislennyi eksperiment, Yanus, M., 1995, 520 pp. | MR

[5] Pashkovskii S., Vychislitelnye primeneniya mnogochlenov i ryadov Chebysheva, Nauka, M., 1983, 384 pp. | MR

[6] Krylov V. I., Priblizhennoe vychislenie integralov, Nauka, M., 1967, 500 pp. | MR

[7] Khubezhty Sh. S., Kvadraturnye formuly dlya singulyarnykh integralov i nekotorye ikh primeneniya, YuMI VNTs RAN, Vladikavkaz, 2011, 232 pp.

[8] Suetin P. K., Klassicheskie ortogonalnye mnogochleny, Nauka, M., 1979, 406 pp.

[9] Natanson I. P., Konstruktivnaya teoriya funktsii, GITTL, M.–L., 1949, 688 pp. | MR

[10] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1984, 750 pp.