Geodesic
On the uniform convergence of the approximate solution of singular integro-differential equation of the first kind
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2013), pp. 54-60 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The article presents the study of the boundary problem for singular integro-differential equation of the first kind with Cauchy kernel. The authors introduce the pair of weight spaces to prove the correctness of the stated problem. The article states the sufficient conditions for the convergence of the general direct method, the method of orthogonal polynomials, and as a result uniform estimates for errors of approximate solution.
Keywords: singular integro-differential equation, approximate solution, correctness of the problem. 
@article{VSGU_2013_6_a5,
     author = {A. V. Ozhegova and L. E. Hajrullina},
     title = {On the uniform convergence of the approximate solution of singular integro-differential equation of the first kind},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {54--60},
     year = {2013},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2013_6_a5/}
}
TY  - JOUR
AU  - A. V. Ozhegova
AU  - L. E. Hajrullina
TI  - On the uniform convergence of the approximate solution of singular integro-differential equation of the first kind
JO  - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
PY  - 2013
SP  - 54
EP  - 60
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/VSGU_2013_6_a5/
LA  - ru
ID  - VSGU_2013_6_a5
ER  - 
%0 Journal Article
%A A. V. Ozhegova
%A L. E. Hajrullina
%T On the uniform convergence of the approximate solution of singular integro-differential equation of the first kind
%J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
%D 2013
%P 54-60
%N 6
%U http://geodesic.mathdoc.fr/item/VSGU_2013_6_a5/
%G ru
%F VSGU_2013_6_a5
A. V. Ozhegova; L. E. Hajrullina. On the uniform convergence of the approximate solution of singular integro-differential equation of the first kind. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2013), pp. 54-60. http://geodesic.mathdoc.fr/item/VSGU_2013_6_a5/

[1] Gabdulkhaev B. G., Pryamye metody resheniya singulyarnykh integralnykh uravnenii I roda, Izd-vo Kazan. un-ta, Kazan, 1994, 285 pp.

[2] Lifanov I. K., Metod singulyarnykh integralnykh uravnenii i chislennyi eksperiment, TOO “Yanus”, M., 1995, 520 pp.

[3] Ozhegova A. V., Ravnomernye priblizheniya reshenii slabo singulyarnykh integralnykh uravnenii pervogo roda, dis. ... kand. fiz.-mat. nauk, Kazan, 1996, 96 pp.

[4] Khairullina L. E., Ravnomernaya skhodimost priblizhennykh reshenii singulyarnogo integralnogo uravneniya pervogo roda s yadrom Koshi, dis. ... kand. fiz.-mat. nauk, Kazan, 2011, 103 pp.

[5] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, 4-e izd., ispr., BVKh-Peterburg, SPb., 2004, 816 pp.

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