Cubature formulas for a two-variable function with boundary-layer components
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- Zadorin, A.I. Comput. Math. and Math. Phys. (2013) 53: 1808. doi:10.1134/S0965542513120130
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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.