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

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 a...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2013-12, Vol.53 (12), p.1808-1818
Main Author: Zadorin, A. I.
Format: Article
Language:English
Subjects:
Approximation
Boundaries
Boundary layer
Computation
Computational mathematics
Computational Mathematics and Numerical Analysis
Construction
Cuba
Estimates
Integrals
Interpolation
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Studies
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Summary: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.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542513120130