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Efficient computation of highly oscillatory integrals with Hankel kernel

Author

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  • Xu, Zhenhua
  • Milovanović, Gradimir V.
  • Xiang, Shuhuang

Abstract

In this paper, we consider the evaluation of two kinds of oscillatory integrals with a Hankel function as kernel. We first rewrite these integrals as the integrals of Fourier-type. By analytic continuation, these Fourier-type integrals can be transformed into the integrals on [0, +∞), the integrands of which are not oscillatory, and decay exponentially fast. Consequently, the transformed integrals can be efficiently computed by using the generalized Gauss–Laguerre quadrature rule. Moreover, the error analysis for the presented methods is given. The efficiency and accuracy of the methods have been demonstrated by both numerical experiments and theoretical results.

Suggested Citation

  • Xu, Zhenhua & Milovanović, Gradimir V. & Xiang, Shuhuang, 2015. "Efficient computation of highly oscillatory integrals with Hankel kernel," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 312-322.
    • Handle: RePEc:eee:apmaco:v:261:y:2015:i:c:p:312-322
    DOI: 10.1016/j.amc.2015.04.006
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    Cited by:

    1. Wang, Hong & Kang, Hongchao & Ma, Junjie, 2024. "An efficient and accurate numerical method for the Bessel transform with an irregular oscillator and its error analysis," Applied Mathematics and Computation, Elsevier, vol. 473(C).
    2. Liu, Guidong & Xiang, Shuhuang, 2019. "Clenshaw–Curtis-type quadrature rule for hypersingular integrals with highly oscillatory kernels," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 251-267.

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