Geodesic
On approximate solution of the Dixon integral equation and some its generalizations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 7, pp. 1161-1169 
A. G. Barseghyan. On approximate solution of the Dixon integral equation and some its generalizations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 7, pp. 1161-1169. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_7_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The paper is devoted to the study and numerical analytical solution of Fredholm-type integral equations of the second kind with symmetric kernels represented by homogeneous functions of degree (-1). The well-known Dixon equation and some its direct generalizations are specially considered. The equations are solved by passing to a Wiener–Hopf equation and applying the kernel averaging method. Results of numerical calculations are presented.

[1] Dixon A. C., “On the solving nuclei of certain integral equation whose nuclei are homogeneous and of degree -1, and the solution of a class of linear functional equations”, Proc. London Math. Soc., 27:2 (1926), 233–272 | MR

[2] Dixon A. C., “Some limiting classes in the theory of integral equations”, Proc. Lond. Math. Soc., 22:2 (1923), 201–222 | MR | Zbl

[3] Titchmarsh E. Ch., Vvedenie v teoriyu integralov Fure, Gostekhizdat, M.–L., 1948

[4] Morse Ph. M., Feschbach H., Methods of theoretical physics, v. I, 1954 | MR

[5] Sakhnovich L. A., “On triangular factorization of positive operators”, Operator Theory: Advances and Applications, 179, Birkhauser Verlag, Basel, 2007, 289–308 | DOI | MR

[6] Krein M. G., “Integralnye uravneniya na polupryamoi s yadrom, zavisyaschim ot raznosti argumentov”, Uspekhi matem. nauk, 13:5(83) (1958), 3–120 | Zbl

[7] Yakubovich S., On the generalized Dixon integral equation, 26 Nov 2014, arXiv: 1411.7244v1

[8] Barsegyan A. G., Engibaryan N. B., “Priblizhennoe reshenie integralnykh i diskretnykh uravnenii Vinera–Khopfa”, Zh. vychisl. matem. i matem. fiz., 55:5 (2015), 836–845 | DOI | Zbl

[9] Arabadzhyan L. G., Engibaryan N. B., “Uravneniya v svertkakh i nelineinye funktsionalnye uravneniya”, Itogi nauki i tekhn. Ser. Matem. analiz., 22, VINITI, M., 1984, 175–244 | Zbl

[10] Gokhberg I. Ts., Feldman I. A., Uravneniya v svertkakh i proektsionnye metody ikh resheniya, Nauka, M., 1971

[11] Polozhii G. N., Chalenko P. I., “Reshenie integralnykh uravnenii metodom polos”, Voprosy matem. fiz. i teorii funktsii, v. 1, K., 1964

[12] Barsegyan A. G., Ter-Avetisyan V. V., “O reshenii uravneniya perenosa v dvizhuscheisya srede”, Astronomicheskii zh., 90:9 (2013), 747–753 | DOI