×

Approximate solution of a singular integral equation using Chebyshev series. (Russian. English summary) Zbl 1474.65489

Summary: 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.

MSC:

65R20 Numerical methods for integral equations
45E05 Integral equations with kernels of Cauchy type
PDFBibTeX XMLCite
Full Text: MNR

References:

[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.
[4] Lifanov I. K., #Metod singulyarnykh integralnykh uravnenii i chislennyi eksperiment, Yanus, M., 1995, 520 pp.
[5] Pashkovskii S., #Vychislitelnye primeneniya mnogochlenov i ryadov Chebysheva, Nauka, M., 1983, 384 pp. · Zbl 0527.65008
[6] Krylov V. I., #Priblizhennoe vychislenie integralov, Nauka, M., 1967, 500 pp.
[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. · Zbl 0449.33001
[9] Natanson I. P., #Konstruktivnaya teoriya funktsii, GITTL, M.-L., 1949, 688 pp.
[10] Kantorovich L. V., Akilov G. P., #Funktsionalnyi analiz, Nauka, M., 1984, 750 pp.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.