Geodesic
Calculation of charges screening an external coaxial electric field on the surface of a conducting axial symmetric body
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 3, pp. 321-327 
A. O. Savchenko; O. Ya. Savchenko. Calculation of charges screening an external coaxial electric field on the surface of a conducting axial symmetric body. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 3, pp. 321-327. http://geodesic.mathdoc.fr/item/SJVM_2012_15_3_a7/
@article{SJVM_2012_15_3_a7,
     author = {A. O. Savchenko and O. Ya. Savchenko},
     title = {Calculation of charges screening an external coaxial electric field on the surface of a~conducting axial symmetric body},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {321--327},
     year = {2012},
     volume = {15},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2012_15_3_a7/}
}
TY  - JOUR
AU  - A. O. Savchenko
AU  - O. Ya. Savchenko
TI  - Calculation of charges screening an external coaxial electric field on the surface of a conducting axial symmetric body
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2012
SP  - 321
EP  - 327
VL  - 15
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SJVM_2012_15_3_a7/
LA  - ru
ID  - SJVM_2012_15_3_a7
ER  - 
%0 Journal Article
%A A. O. Savchenko
%A O. Ya. Savchenko
%T Calculation of charges screening an external coaxial electric field on the surface of a conducting axial symmetric body
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2012
%P 321-327
%V 15
%N 3
%U http://geodesic.mathdoc.fr/item/SJVM_2012_15_3_a7/
%G ru
%F SJVM_2012_15_3_a7

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

A one-dimensional integral equation for finding charges on the surface of a conducting axially symmetric body is given. For the case of an ellipsoid of rotation in the electric field with polynomial values on the axis of symmetry an exact solution is obtained. The axis of symmetry of the body and the axis of the external field coincide with each other. A numerical algorithm, based on a combination of the projective method and the method of iterative regularization for solving the first kind Fredholm equations, is proposed. The projectors were chosen as B-splines. The charges calculated for the ellipsoid of rotation are close to analytical ones.

[1] Savchenko A. O., Savchenko O. Ya., “Poverkhnostnye toki sverkhprovodyaschego osesimmetrichnogo tela, ekraniruyuschie vneshnee soosnoe magnitnoe pole”, Zh. tekhnicheskoi fiziki (S-Pb), 77:7 (2007), 130–133

[2] Savchenko A. O., Savchenko O. Ya., “Vychislenie tokov na poverkhnosti sverkhprovodyaschego osesimmetrichnogo tela, ekraniruyuschikh vneshnee soosnoe magnitnoe pole”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 10:3 (2007), 317–324

[3] Erdelyi A., “Singularities of generalized axially symmetric potentials”, Communications on Pure and Applied Mathematics, 9 (1956), 403–414 | DOI | MR | Zbl

[4] Lavrentev M. M., O nekotorykh nekorrektnykh zadachakh matematicheskoi fiziki, Izd-vo SO AN SSSR, Novosibirsk, 1962 | MR

[5] Bernshtein S. N., Ekstremalnye svoistva polinomov i nailuchshee priblizhenie nepreryvnykh funktsii odnoi veschestvennoi peremennoi, GROTL, L.-M., 1937

[6] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1972 | MR | Zbl

[7] Verlan A. F., Sizikov V. S., Integralnye uravneniya: metody, resheniya, algoritmy, Naukova dumka, Kiev, 1986 | MR

[8] Shikin E. V., Plis A. I., Krivye i poverkhnosti na ekrane kompyutera, Rukovodstvo po splainam dlya polzovatelei, Dialog-MIFI, M., 1996