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On the numerical approximation for Fourier-type highly oscillatory integrals with Gauss-type quadrature rules

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  • He, Guo
  • Zhang, Chuanlin

Abstract

In this paper, we present an improved numerical steepest descent method for the approximation of Fourier-type highly oscillatory integrals. Based on the previous numerical steepest descent method, the new method used the integrand information at endpoints and stationary points. The asymptotic order is given that is improved both for the case of stationary points and stationary points free. Several numerical examples are presented which show the high efficiency of the proposed method. Numerical results support our theoretical analyses.

Suggested Citation

  • He, Guo & Zhang, Chuanlin, 2017. "On the numerical approximation for Fourier-type highly oscillatory integrals with Gauss-type quadrature rules," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 96-104.
    • Handle: RePEc:eee:apmaco:v:308:y:2017:i:c:p:96-104
    DOI: 10.1016/j.amc.2017.03.021
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    Cited by:

    1. Kang, Hongchao & Xu, Qi, 2023. "Quadrature formulae of many highly oscillatory Fourier-type integrals with algebraic or logarithmic singularities and their error analysis," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    2. Kang, Hongchao, 2019. "Efficient calculation and asymptotic expansions of many different oscillatory infinite integrals," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 305-318.

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