Geodesic
Justification of the Galerkin method for hypersingular equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 3, pp. 432-440 
S. I. Eminov; V. S. Eminova. Justification of the Galerkin method for hypersingular equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 3, pp. 432-440. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_3_a9/
@article{ZVMMF_2016_56_3_a9,
     author = {S. I. Eminov and V. S. Eminova},
     title = {Justification of the {Galerkin} method for hypersingular equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {432--440},
     year = {2016},
     volume = {56},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_3_a9/}
}
TY  - JOUR
AU  - S. I. Eminov
AU  - V. S. Eminova
TI  - Justification of the Galerkin method for hypersingular equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2016
SP  - 432
EP  - 440
VL  - 56
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_3_a9/
LA  - ru
ID  - ZVMMF_2016_56_3_a9
ER  - 
%0 Journal Article
%A S. I. Eminov
%A V. S. Eminova
%T Justification of the Galerkin method for hypersingular equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2016
%P 432-440
%V 56
%N 3
%U http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_3_a9/
%G ru
%F ZVMMF_2016_56_3_a9

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper presents a theoretical study of hypersingular equations of the general form for problems of electromagnetic-wave diffraction on open surfaces of revolution. Justification of the Galerkin is given. The method is based on the separation of the principal term and its analytic inversion. The inverse of the principal operator is completely continuous. On the basis of this result, the equivalence of the initial equation to a Fredholm integral equation of the second kind is proven. An example of numerical solution with the use of Chebyshev polynomials of the second kind is considered.

[1] Vasilev E. H., Vozbuzhdenie tel vrascheniya, Radio i svyaz, M., 1987

[2] Eminov S. I., “Teoriya integralnogo uravneniya tonkogo vibratora”, Radiotekhn. i elektronika, 38:12 (1993), 2160–2168

[3] Vladimirov V. S., Uravneniya matematicheskoi fiziki, 4-e izd., Fizmatlit, M., 1981

[4] Gradshtein I. S., Ryzhik I. M., Tablitsy integralov, summ, ryadov i proizvedenii, Fizmatlit, M., 1962

[5] Mikhlin S. G., Variatsionnye metody v matematicheskoi fizike, Nauka, M., 1970 | MR

[6] Panasyuk V. V., Savruk M. P., Nazarchuk Z. T., Metod singulyarnykh integralnykh uravnenii v dvumernykh zadachakh difraktsii, Nauk. dumka, Kiev, 1984 | MR

[7] Vainikko G. M., Lifanov I. K., Poltavskii L. N., Chislennye metody v gipersingulyarnykh integralnykh uravneniyakh i ikh prilozheniya, Yanus-K, M., 2001

[8] V. A. Trenogin, Funktsionalnyi analiz, Nauka, M., 1980 | MR