Computational Mathematics and Mathematical Physics

, Volume 53, Issue 12, pp 1808-1818

First online:

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

  • A. I. ZadorinAffiliated withOmsk Branch of the Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences Email author 

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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.


two-variable function boundary layer double integral nonpolynomial interpolation cubature rule error estimate