Special versions of the collocation method for a~class of integral equations of the third kind
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2012), pp. 27-33.

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In this paper we propose and justify special direct methods for the approximate solution of equations of the third kind in the space of distributions.
Keywords: third-kind integral equation, space of distributions, approximate solution, theoretical substantiation.
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N. S. Gabbasov; S. A. Solov'eva. Special versions of the collocation method for a~class of integral equations of the third kind. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2012), pp. 27-33. http://geodesic.mathdoc.fr/item/IVM_2012_8_a2/

[1] 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

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

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

[4] Soloveva S. A., O pryamykh metodakh resheniya integralnykh uravnenii tretego roda v prostranstve obobschennykh funktsii, Diss. $\dotsc$ kand. fiz.-matem. nauk, KGU, Kazan, 2007

[5] Natanson I. P., Konstruktivnaya teoriya funktsii, Gostekhizdat, L., 1949

[6] Kaspitskaya M. F., Tukalevskaya N. I., “K voprosu o skhodimosti metoda kollokatsii”, Ukr. matem. zhurn., 19:4 (1967), 48–56 | MR

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

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

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

[10] Petersen I., “O skhodimosti priblizhennykh metodov interpolyatsionnogo tipa dlya obyknovennykh differentsialnykh uravnenii”, Izv. AN EstSSR. Ser. fiz.-matem. i tekh. nauk, 1961, no. 1, 3–12 | Zbl