Special variants of collocation method for integral equations in a special case
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2017), pp. 45-53.

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We study integral equation of the third kind with fixed singularities in the kernel. For approximate solving of these equations in the space of generalized functions we propose and substantiate a new generalized variants of the collocation method.
Keywords: integral equation of the third kind, space of generalized functions, approximate solution, collocation method, theoretical substantiation.
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N. S. Gabbasov; R. R. Zamaliev. Special variants of collocation method for integral equations in a special case. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2017), pp. 45-53. http://geodesic.mathdoc.fr/item/IVM_2017_5_a4/

[1] Adamar Zh., Zadacha Koshi dlya lineinykh uravnenii s chastnymi proizvodnymi giperbolicheskogo tipa, Nauka, M., 1978

[2] Bart G. R., Warnock R. L., “Linear integral equations of the third-kind”, SIAM J. Math. Anal., 4:4 (1973), 609–622 | DOI | MR | Zbl

[3] Keiz K. M., Tsvaifel P. F., Lineinaya teoriya perenosa, Mir, M., 1972

[4] Zamaliev R. R., O pryamykh metodakh resheniya integralnykh uravnenii tretego roda s osobennostyami v yadre, Diss. $\dots$ kand. fiz.-matem. nauk, KFU, Kazan, 2012

[5] Bzhikhatlov Kh. G., “Ob odnoi kraevoi zadache so smescheniem”, Differents. uravneniya, 9:1 (1973), 162–165 | Zbl

[6] Gabbasov N. S., “Metody resheniya integralnogo uravneniya tretego roda s fiksirovannymi osobennostyami v yadre”, Differents. uravneniya, 45:9 (2009), 1341–1348 | Zbl

[7] Gabbasov N. S., Zamaliev R. R., “Novye varianty splain-metodov dlya integralnykh uravnenii tretego roda s osobennostyami v yadre”, Differents. uravneniya, 46:9 (2010), 1320–1328 | Zbl

[8] Gabbasov N. S., Zamaliev R. R., “Novyi variant metoda podoblastei dlya integralnykh uravnenii tretego roda s osobennostyami v yadre”, Izv. vuzov. Matem., 2011, no. 5, 12–18

[9] Gabbasov N. S., “Novyi variant metoda kollokatsii dlya odnogo klassa integralnykh uravnenii v osobom sluchae”, Differents. uravneniya, 49:9 (2013), 1178–1185 | Zbl

[10] Gabbasov N. S., “Spetsialnyi pryamoi metod resheniya integralnykh uravnenii v osobom sluchae”, Differents. uravneniya, 50:9 (2014), 1245–1252 | DOI | Zbl

[11] Gabdulkhaev B. G., Optimalnye approksimatsii reshenii lineinykh zadach, Izd-vo Kazansk. un-ta, Kazan, 1980

[12] Prësdorf Z., “Singulyarnoe integralnoe uravnenie s simvolom, obraschayuschimsya v nul v konechnom chisle tochek”, Matem. issledovaniya, 7:1 (1972), 116–132 | Zbl

[13] Gabbasov N. S., Metody resheniya integralnykh uravnenii Fredgolma v prostranstvakh obobschennykh funktsii, Izd-vo Kazansk. un-ta, Kazan, 2006

[14] Natanson I. P., Konstruktivnaya teoriya funktsii, Gostekhizdat, M.–L., 1949 | MR

[15] Petersen I., “O skhodimosti priblizhennykh metodov interpolyatsionnogo tipa dlya obyknovennykh differentsialnykh uravnenii”, Izv. AN ESSR. Ser. fiz.-mat. i tekhn. nauk, 1961, no. 1, 3–12