Geodesic
Calculation of currents on the surface of a~superconducting axially symmetric body screening an external coaxial magnetic field
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 3, pp. 317-324.

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A one-dimensional integral equation for the finding of currents on the surface of a superconducting axially symmetric body is given. For the case of an ellipsoid of rotation in a homogeneous magnetic field and for a sphere in a magnetic 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 magnetic field coincide. A numerical algorithm based on a combination of a projective method and an iterative regularization method to solve first kind Fredholm equations is proposed. $B$-splines were chosen as projectors. The results of a numerical reconstruction of the sought-for functions for some particular cases with the use of the method proposed are presented. 
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     title = {Calculation of currents on the surface of a~superconducting axially symmetric body screening an external coaxial magnetic field},
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A. O. Savchenko; O. Ya. Savchenko. Calculation of currents on the surface of a~superconducting axially symmetric body screening an external coaxial magnetic field. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 10 (2007) no. 3, pp. 317-324. http://geodesic.mathdoc.fr/item/SJVM_2007_10_3_a8/

[1] Landau L. D., Lifshits E. M., Elektrodinamika sploshnykh sred, Nauka, M., 1992 | MR

[2] Vorobev N. I., Zubkov P. I. i dr., Zadachi po fizike, ed. O. Ya. Savchenko, izd-vo Lan, SPb., 2001

[3] Arthur Erdelyi, “Singularities of Generalized Axially Symmetric Potentials”, Communications on Pure and Applied Mathematics, 9 (1956), 403–414 | DOI | MR | Zbl

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

[5] Verlan A. F., Sizikov V. S., Integralnye uravneniya: Metody, resheniya, algoritmy, Naukova Dumka, Kiev, 1986 | MR

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

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

[8] Urev M. V., “Algoritm chislennogo prodolzheniya obobschennogo osesimmetrichnogo potentsiala s osi simmetrii”, ZhVMiMF, 25:2 (1985), 269–282 | MR | Zbl

[9] Bernshtein S. N., Ekstremalnye svoistva polinomov i nailuchshee priblizhenie nepreryvnykh funktsii odnoi veschestvennoi peremennoi, GONTI, M., 1937