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Modification of the Euler quadrature formula for functions with a boundary-layer component

Abstract

The Euler quadrature formula for the numerical integration of functions with a boundary-layer component on a uniform grid is investigated. If the function under study has a rapidly growing component, the error can be significant. A uniformly accurate quadrature formula is constructed by modifying the Hermite interpolation formula so that the resulting one is exact for the boundary-layer component. An analogue of the Euler formula that is exact for the boundary-layer component is constructed. It is proved that the resulting composite quadrature formula is third-order accurate in space uniformly with respect to the boundary-layer component and its derivatives.

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Correspondence to A. I. Zadorin.

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Original Russian Text © A.I. Zadorin, 2014, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2014, Vol. 54, No. 10, pp. 1547–1556.

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Zadorin, A.I. Modification of the Euler quadrature formula for functions with a boundary-layer component. Comput. Math. and Math. Phys. 54, 1489–1498 (2014). https://doi.org/10.1134/S0965542514100078

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  • DOI: https://doi.org/10.1134/S0965542514100078

Keywords

  • quadrature formula for definite integrals
  • function with a boundary-layer component
  • modified Euler quadrature formula
  • Hermite polynomial
  • modification
  • error estimate for quadrature formulas