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Quadrature formulas for functions with a boundary-layer component

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Abstract

Quadrature formulas for one-variable functions with a boundary-layer component are constructed and studied. It is assumed that the integrand can be represented as the sum of a regular and a boundary-layer component, the latter having high gradients that reduce the accuracy of classical quadrature formulas, such as the trapezoidal and Simpson rules. The formulas are modified so that their error is independent of the gradients of the boundary-layer component. Results of numerical experiments are presented.

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Authors and Affiliations

  1. Omsk Branch of the Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, ul. Pevtsova 13, Omsk, 644099, Russia

    A. I. Zadorin

  2. Omsk State University, pr. Mira 55a, Omsk, 644077, Russia

    N. A. Zadorin

Authors
  1. A. I. Zadorin
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  2. N. A. Zadorin
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Correspondence to A. I. Zadorin.

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Original Russian Text © A.I. Zadorin, N.A. Zadorin, 2011, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2011, Vol. 51, No. 11, pp. 1952–1962.

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Zadorin, A.I., Zadorin, N.A. Quadrature formulas for functions with a boundary-layer component. Comput. Math. and Math. Phys. 51, 1837–1846 (2011). https://doi.org/10.1134/S0965542511110157

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  • DOI: https://doi.org/10.1134/S0965542511110157

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