Literature cited
N. I. Muskhelishvili, Singular Integral Equations [in Russian], Nauka, Moscow (1968).
V. V. Ivanov, Theory of Approximate Methods and Its Application to the Numerical Solution of Singular Integral Equations [in Russian], Naukova Dumka, Kiev (1968).
B. G. Gabdulkhaev, “The approximate solution of singular integral equations by the method of mechanical quadratures,” Dokl. Akad. Nauk SSSR,179, No. 2, 260–263 (1968).
S. Prössdorf and B. Silberman, Projektionsverfahren und die Näherungsweise Lösung Singularer Gleichungen, Teubner, Leipzig (1977).
D. Elliott, “The approximate solution of singular integral equations,” in: Solution Methods for Integral Equations, Plenum Press, New York (1979), pp. 83–107.
B. G. Gabdulkhaev, “Finite-dimensional approximations of singular integrals and direct methods for solving singular integral and integrodifferential equations,” J. Sov. Math.,18, No. 4 (1982).
B. G. Gabdulkhaev, Optimal Approximations of Solutions of Linear Problems [in Russian], Kazan State Univ. (1980).
K. I. Babenko, “On an approach to estimating the quality of computational algorithms,” Preprint No. 7, Inst. Prikl. Mat., Akad. Nauk SSSR, Moscow (1974).
K. I. Babenko, “Several remarks on the discretization of elliptic problems,” Dokl. Akad. Nauk SSSR,221, No. 1, 11–14 (1975).
B. V. Khvedelidze, “Linear discontinuous boundary value problems of the theory of functions, singular integral equations, and some of their applications,” Trudy Tbilissk. Mat. Inst. Akad. Nauk GSSR,23 (1957).
F. D. Gakhov, Boundary Value Problems, Pergamon (1974).
L. I. Chibrikova, Fundamental Boundary Value Problems for Analytic Functions [in Russian], Kazan Univ. (1977).
A. I. Guseinov and Kh. Sh. Mukhtarov, Introduction to the Theory of Nonlinear Singular Integral Equations [in Russian], Nauka, Moscow (1980).
A. N. Tikhonov and V. Ya. Arsenin, Solutions of Ill-Posed Problems [in Russian], Nauka, Moscow (1979).
V. V. Ivanov, “On the approximate determination of the eigenvalues and of all solutions of singular integral equations,” in: Materials of the Scientific-Technical Conference, Izd. Akad. Nauk UkrSSR, Kiev (1960).
I. K. Lifanov, “On the ill-posedness and regularization of the numerical solution of singular integral equations of the first kind,” Dokl. Akad. Nauk SSSR,255, No. 5, 1046–1050 (1980).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 41, No. 5, pp. 693–709, May, 1987.
Rights and permissions
About this article
Cite this article
Babaev, A.A., Musaev, B.I. An approximate solution of a complete linear singular integral equation with the Hilbert kernel. Mathematical Notes of the Academy of Sciences of the USSR 41, 389–399 (1987). https://doi.org/10.1007/BF01159864
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01159864