Cubature formulas for a two-variable function with boundary-layer components
- A. I. Zadorin
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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.
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- Cubature formulas for a two-variable function with boundary-layer components
Computational Mathematics and Mathematical Physics
Volume 53, Issue 12 , pp 1808-1818
- Cover Date
- Print ISSN
- Online ISSN
- Springer US
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- two-variable function
- boundary layer
- double integral
- nonpolynomial interpolation
- cubature rule
- error estimate
- A. I. Zadorin (1)
- Author Affiliations
- 1. Omsk Branch of the Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, ul. Pevtsova 13, Omsk, 644043, Russia