, Volume 53, Issue 12, pp 1808-1818
Date: 27 Dec 2013

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.

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