Error estimation for solution of Abel equation on sets of monotonic and convex functions
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 6 (2003) no. 2, pp. 171-180.

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We consider Abel equation under condition that the exact solution belongs to a compact set. The error of finite-dimensional approximation of the problem is estimated. For the error obtained we construct an area to which the exact and the approximate solutions belong using the method of cutting convex polyhedrons.
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N. N. Nikolaeva; V. N. Titarenko; A. G. Yagola. Error estimation for solution of Abel equation on sets of monotonic and convex functions. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 6 (2003) no. 2, pp. 171-180. http://geodesic.mathdoc.fr/item/SJVM_2003_6_2_a6/

[1] Antokhin I. I., Cherepashchuk A. M., Yagola A. G., “Velocity law in the extended photosphere of the WN5 star in the eclipsing binary V444 Cygni”, Astrophysics and Space Science, 354 (1997), 111–131 | DOI

[2] Rychagov M., Tereshchenko S., “Multipath flowrate measurements of symmetric and asymmetric flows”, Inverse Problems, 16 (2000), 495–504 | DOI | Zbl

[3] Anderssen R. S., Application and numerical solution of Abel-type integral equation, Technical Summary Report; 1787, University of Wisconsin-Madison, Mathematics Research Center, 1977

[4] Tikhonov A. N., Goncharskii A. V., Stepanov V. V., Yagola A. G., Chislennye metody resheniya nekorrektnykh zadach, Nauka, M., 1990 | MR

[5] Tikhonov A. N., Leonov A. S., Yagola A. G., Nelineinye nekorrektnye zadachi, Nauka, M., 1995 | MR

[6] Gorenflo R., Vessella S., Abel integral equations. Analysis and applications, Springer, Berlin, 1991 | MR

[7] Ivanov V. K., Vasin V. V., Tanana V. P., Teoriya lineinykh nekorrektnykh zadach i ee prilozheniya, Nauka, M., 1978 | MR

[8] Vasilev F. P., Ivanitskii A. Yu., Lineinoe programmirovanie, Faktorial, M., 1998 | MR

[9] Titarenko V. N., Yagola A. G., “Metod otsecheniya vypuklykh mnogogrannikov i ego primenenie k nekorrektnym zadacham”, Vychislitelnye metody i programmirovanie, 1 (2000), 8–13