Geodesic
Special variants of collocation method for integral equations in a special case
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2017), pp. 45-53 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{IVM_2017_5_a4,
     author = {N. S. Gabbasov and R. R. Zamaliev},
     title = {Special variants of collocation method for integral equations in a special case},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {45--53},
     year = {2017},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_5_a4/}
}
TY  - JOUR
AU  - N. S. Gabbasov
AU  - R. R. Zamaliev
TI  - Special variants of collocation method for integral equations in a special case
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2017
SP  - 45
EP  - 53
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/IVM_2017_5_a4/
LA  - ru
ID  - IVM_2017_5_a4
ER  - 
%0 Journal Article
%A N. S. Gabbasov
%A R. R. Zamaliev
%T Special variants of collocation method for integral equations in a special case
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2017
%P 45-53
%N 5
%U http://geodesic.mathdoc.fr/item/IVM_2017_5_a4/
%G ru
%F IVM_2017_5_a4
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