Geodesic
Approximate solution of Wiener–Hopf integral equations and its discrete counterparts
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 5, pp. 836-845 
A. G. Barseghyan; N. B. Engibaryan. Approximate solution of Wiener–Hopf integral equations and its discrete counterparts. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 5, pp. 836-845. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_5_a9/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A method for averaging the kernel of a numerical-analytical solution of nonsingular Wiener–Hopf (WH) equations is proposed. By applying a discretization technique similar to the strip method, the WH integral equation is reduced to a discrete WH equation. A priori estimates are obtained that ensure the uniform convergence of the method. Two techniques for solving discrete WH equations are developed. The first is based on reducing these equations to finite-diagonal systems with a solution converging in the norm to the solution of the original equation. The second method is based on a modification of the Baxter projection theorem, whereby the strongly converging reduction procedure can be replaced by one converging in the norm.

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

[2] Gakhov F. D., Cherskii Yu. I., Uravneniya tipa svertki, Nauka, M., 1978

[3] Presdorf Z., Nekotorye klassy singulyarnykh uravnenii, Mir, M., 1979

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

[5] Atkinson K. E., A survey of numerical methods for the solution of Fredholm integral equations of the second kind, Soc. Industrial and Appl. Math., Philadelphia, Pa, 1976 | MR | Zbl

[6] Vainikko G. M., “Regulyarnaya skhodimost operatorov i priblizhennoe reshenie uravnenii”, Itogi nauki i tekhn. Ser. Matem. analiz, 16, 1979, 5–53

[7] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1977

[8] Matematicheskaya Entsiklopediya, v. 4, Sov. entsiklopediya, M., 1984

[9] Engibaryan N. B., Mnatsakanyan M. A., “Lineinye algebraicheskie sistemy s teplitsevymi matritsami”, Zh. vychisl. matem. i matem. fiz., 17:5 (1977), 1102–1116 | MR | Zbl

[10] Zigmund A., Trigonometricheskie ryady, v. 1, Mir, M., 1965 | MR

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