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An analogue of the four-point Newton-Cotes formula for a function with a boundary-layer component


The construction of the Newton-Cotes formulas is based on approximating the integrand by a Lagrange polynomial. The error of such quadrature formulas can be great for a function with a boundary-layer component. In this paper, an analog of the four-point Newton-Cotes rule is constructed. The construction is based on using a nonpolynomial interpolation that is exact for the boundary layer component. Error estimates of the quadrature rule independent of the boundary layer component gradients are obtained. Numerical experiments are performed.

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Correspondence to A. I. Zadorin.

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Original Russian Text © A.I. Zadorin, N.A. Zadorin, 2013, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2013, Vol. 16, No. 4, pp. 313–323.

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Zadorin, A.I., Zadorin, N.A. An analogue of the four-point Newton-Cotes formula for a function with a boundary-layer component. Numer. Analys. Appl. 6, 268–278 (2013).

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  • one-variable function
  • boundary-layer component
  • high gradients
  • definite integral
  • nonpolynomial interpolation
  • quadrature rule
  • error estimate