Geodesic
The method of mechanical quadratures for integral equations with fixed singularity
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2016), pp. 83-91

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We investigate the method of mechanical quadratures for integral equations with fixed singularity. We establish estimates of the error of this method based on a quadrature process, which is the best in the class of differentiable functions. We prove the convergence of the method in finite-dimensional and uniform metrics. We find that the investigated quadrature method is optimal by order on the Hölder class of functions.
Keywords: integral equation, accuracy, optimality.
Mots-clés : quadrature process, solution, convergence 
@article{IVM_2016_7_a8,
     author = {L. A. Onegov},
     title = {The method of mechanical quadratures for integral equations with fixed singularity},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {83--91},
     publisher = {mathdoc},
     number = {7},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_7_a8/}
}
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L. A. Onegov. The method of mechanical quadratures for integral equations with fixed singularity. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2016), pp. 83-91. http://geodesic.mathdoc.fr/item/IVM_2016_7_a8/