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Quadrature formulas for functions with a boundary-layer component


Quadrature formulas for one-variable functions with a boundary-layer component are constructed and studied. It is assumed that the integrand can be represented as the sum of a regular and a boundary-layer component, the latter having high gradients that reduce the accuracy of classical quadrature formulas, such as the trapezoidal and Simpson rules. The formulas are modified so that their error is independent of the gradients of the boundary-layer component. Results of numerical experiments are presented.

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Correspondence to A. I. Zadorin.

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Original Russian Text © A.I. Zadorin, N.A. Zadorin, 2011, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2011, Vol. 51, No. 11, pp. 1952–1962.

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Zadorin, A.I., Zadorin, N.A. Quadrature formulas for functions with a boundary-layer component. Comput. Math. and Math. Phys. 51, 1837–1846 (2011).

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