Computational Mathematics and Mathematical Physics

, Volume 53, Issue 12, pp 1808–1818

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

Article

DOI: 10.1134/S0965542513120130

Cite this article as:
Zadorin, A.I. Comput. Math. and Math. Phys. (2013) 53: 1808. doi:10.1134/S0965542513120130
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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.

Keywords

two-variable functionboundary layerdouble integralnonpolynomial interpolationcubature ruleerror estimate

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Omsk Branch of the Sobolev Institute of Mathematics, Siberian BranchRussian Academy of SciencesOmskRussia