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

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 th...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2014-10, Vol.54 (10), p.1489-1498
Main Author: Zadorin, A. I.
Format: Article
Language:English
Subjects:
Boundaries
Computational mathematics
Computational Mathematics and Numerical Analysis
Construction
Derivatives
Error analysis
Eulers equations
Interpolation
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Polynomials
Quadratures
Studies
Citations: Items that this one cites
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Summary: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.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542514100078