Geodesic
A constructive method for the solution of integral equations with Hilbert kernel
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 4, pp. 14-25 Cet article a éte moissonné depuis la source Math-Net.Ru

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We propose and prove a constructive method for the solution of linear singular integral equations with Hilbert kernel. In this method, in contrast to the methods applied earlier, the singular operator is approximated by operators that preserve the main properties of this operator, which makes it possible to obtain estimates that are more exact from the point of view of convergence rate. In addition, this method requires less computations because it allows one to find approximate solutions explicitly (not only at isolated points) and the coefficients of the corresponding systems of algebraic equations are easily calculated.
Keywords: singular integral equation, constructive method, approximation of a singular integral, best mean-square approximation.
Mots-clés : Hilbert kernel 
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R. A. Aliev; A. F. Amrakhova. A constructive method for the solution of integral equations with Hilbert kernel. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 4, pp. 14-25. http://geodesic.mathdoc.fr/item/TIMM_2012_18_4_a1/

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