On quadrature of highly oscillatory integrals with logarithmic singularities
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摘要
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.
论文关键词:Numerical integration,Oscillatory function,Interpolation polynomial,Logarithmic singularities,Error analysis
论文评审过程:Received 28 March 2015, Revised 27 May 2015, Accepted 6 June 2015, Available online 24 June 2015, Version of Record 24 June 2015.
论文官网地址:https://doi.org/10.1016/j.amc.2015.06.014