A direct method for solving integral equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2010), pp. 14-19.

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In this paper we theoretically justify the Bogolyubov–Krylov method for weakly singular integral equations.
Keywords: weakly singular integral equations, spline-collocation method, Bogolyubov–Krylov method.
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S. R. Enikeeva. A direct method for solving integral equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2010), pp. 14-19. http://geodesic.mathdoc.fr/item/IVM_2010_2_a1/

[1] Kantorovich L. V., Krylov V. I., Priblizhennye metody vysshego analiza, Fizmatgiz, M., 1962, 708 pp. | MR

[2] Gabdulkhaev B. G., “Approksimatsiya polinomami i splainami reshenii slabo singulyarnykh integralnykh uravnenii”, Teoriya priblizheniya funktsii, Nauka, M., 1977, 89–93 | MR

[3] Gabdulkhaev B. G., Optimalnye approksimatsii reshenii lineinykh zadach, Izd-vo Kazansk. un-ta, Kazan, 1980, 232 pp. | MR

[4] Gabdulkhaev B. G., Pryamye metody resheniya singulyarnykh integralnykh uravnenii $\mathrm I$ roda, Izd-vo Kazansk. un-ta, Kazan, 1994, 288 pp. | MR

[5] Gabdulkhaev B. G., Chislennyi analiz singulyarnykh integralnykh uravnenii. Izbrannye glavy, Izd-vo Kazansk. un-ta, Kazan, 1995, 230 pp. | MR

[6] Gabdulkhaev B. G., Akhmetov S. M., “O metode splain-kollokatsii dlya integralnykh uravnenii”, Prilozheniya funktsionalnogo analiza k priblizhennym vychisleniyam, Izd-vo Kazansk. un-ta, Kazan, 1974, 7–14 | MR

[7] Gabdulkhaev B. G., Gorlov V. E., “O skhodimosti poligonalnogo metoda resheniya slabo singulyarnykh integralnykh uravnenii”, Funktsionalnyi analiz i ego prilozheniya, Izd-vo Kazansk. un-ta, Kazan, 1975, 60–72

[8] Gabdulkhaev B. G., Dushkov P. N., “O poligonalnom metode resheniya integralnykh uravnenii so slaboi osobennostyu”, Prilozheniya funktsionalnogo analiza k priblizhennym vychisleniyam, Izd-vo Kazansk. un-ta, Kazan, 1974, 37–57

[9] Gabdulkhaev B. G., Zhechev I. I., “Poligonalnyi metod resheniya lineinykh uravnenii”, Nauchni trudove Vissh. ped. in-t (Plodiv), 1971, no. 1, 9–26

[10] Gabdulkhaev B. G., “Reshenie operatornykh i integralnykh uravnenii metodom Bogolyubova–Krylova”, Izv. vuzov. Matematika, 2002, no. 10, 34–47 | MR | Zbl

[11] Galishnikova T. N., Ilinskii A. S., Chislennye metody v zadachakh difraktsii, Izd-vo MGU, M., 1987, 208 pp. | MR | Zbl

[12] Tsetsokho V. A., Chislennoe reshenie zadach difraktsii metodom potentsialov, Diss. $\dots$ d-ra fiz.-matem. nauk v forme nauchn. dokl., Novosibirsk, 1987, 38 pp.

[13] Korneichuk N. P., Splainy v teorii priblizheniya, Nauka, M., 1984, 352 pp. | MR