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Cubature formulas for a two-variable function with boundary-layer components

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Abstract

Cubature formulas for evaluating the double integral of a two-variable function with boundary-layer components are constructed and studied. Because of the boundary-layer components, the cubature formulas based on Newton-Cotes formulas become considerably less accurate. Analogues of the trapezoidal and Simpson rules that are exact for the boundary-layer components are constructed. Error estimates for the constructed formulas are derived that are uniform in the gradients of the integrand in the boundary layers.

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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, 644043, Russia

    A. I. Zadorin

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  1. A. I. Zadorin
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Correspondence to A. I. Zadorin.

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Original Russian Text © A.I. Zadorin, 2013, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2013, Vol. 53, No. 12, pp. 1997–2007.

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Zadorin, A.I. Cubature formulas for a two-variable function with boundary-layer components. Comput. Math. and Math. Phys. 53, 1808–1818 (2013). https://doi.org/10.1134/S0965542513120130

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  • DOI: https://doi.org/10.1134/S0965542513120130

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