Efficient methods for highly oscillatory integrals with weakly singular and hypersingular kernels

Bin Li and Shuhuang Xiang

Applied Mathematics and Computation, 2019, vol. 362, issue C, -

Abstract: In this paper, we present a special Clenshaw–Curtis Filon (CCF) type scheme for approximation of highly oscillatory integrals with weak and hypersingular kernels. The non-oscillatory and nonsingular part of the integrand is replaced by a special Hermite interpolation polynomial. Error bounds with respect to the frequency k and the number of the Clenshaw–Curtis points N are considered. The overall computational complexity for the scheme is O(Nlog (N)). Numerical experiments support the theoretical analysis.

Keywords: Hypersingular; Filon–Clenshaw–Curtis method; Highly oscillatory; Gauss–Laguerre quadrature; Hermite interpolation polynomial (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:362:y:2019:i:c:18

DOI: 10.1016/j.amc.2019.06.013

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