Special version of the subdomain method for a~class of integral equations of the third kind in the space of generalized functions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2014), pp. 49-55.

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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 general case of zeros of the coefficient in the space of distributions, based on Kantorovich polynomials.
Keywords: third kind integral equation, space of distributions, approximate solution, theoretical substantiation
Mots-clés : subdomain method.
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N. S. Gabbasov; S. A. Solov'eva. Special version of the subdomain method for a~class of integral equations of the third kind in the space of generalized functions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2014), pp. 49-55. http://geodesic.mathdoc.fr/item/IVM_2014_7_a3/

[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 KGU, Kazan, 2006

[4] Gabbasov N. S., Soloveva S. A., “K teorii razreshimosti integralnykh uravnenii tretego roda”, Trudy Vtoroi Vserossiiskoi nauchnoi konferentsii (1–3 iyunya 2005 g.). Chast 3, Differentsialnye uravneniya i kraevye zadachi, Matem. modelirovanie i kraev. zadachi, SamGTU, Samara, 2005, 68–72

[5] Soloveva S. A., “Obobschennyi metod podoblastei dlya odnogo klassa integralnykh uravnenii tretego roda”, Trudy Tretei Vserossiiskoi nauchnoi konferentsii (29–31 maya 2006 g.). Chast 3, Differentsialnye uravneniya i kraevye zadachi, Matem. modelirovanie i kraev. zadachi, SamGTU, Samara, 2006, 209–212

[6] Gabbasov N. S., Soloveva S. A., “Obobschennyi metod momentov dlya odnogo klassa integralnykh uravnenii tretego roda”, Differents. uravneniya, 42:10 (2006), 1416–1423 | MR | Zbl

[7] Gabbasov N. S., Soloveva S. A., “O splain-metode resheniya integralnykh uravnenii tretego roda”, Izv. vuzov. Matem., 2007, no. 3, 3–11 | MR | Zbl

[8] Gabbasov N. S., Soloveva S. A., “O spetsialnykh variantakh metoda kollokatsii dlya odnogo klassa integralnykh uravnenii tretego roda”, Izv. vuzov. Matem., 2012, no. 8, 27–33 | MR | Zbl

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

[10] Uzhdavinis I. V., “O skhodimosti metoda tipa podoblastei”, Differents. uravneniya i ikh primenenie, 1971, no. 1, 73–83

[11] Gabdulkhaev B. G., Optimalnye approksimatsii reshenii lineinykh zadach, Izd-vo KGU, Kazan, 1980 | MR

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

[13] Edvards R., Funktsionalnyi analiz, 2-e izd., Mir, M., 1971