On quadrature of highly oscillatory integrals with logarithmic singularities

Ruyun Chen and Xiaoliang Zhou

Applied Mathematics and Computation, 2015, vol. 265, issue C, 973-982

Abstract: In this paper a quadrature rule is discussed for highly oscillatory integrals with logarithmic singularities. At the same time, its error depends on the frequency ω and the computation of its moments are given. The new rule is implemented by interpolating f at Chebyshev nodes and singular point where the interpolation polynomial satisfies some conditions. Numerical experiments conform the efficiency for obtaining the approximations.

Keywords: Numerical integration; Oscillatory function; Interpolation polynomial; Logarithmic singularities; Error analysis (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:265:y:2015:i:c:p:973-982

DOI: 10.1016/j.amc.2015.06.014

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