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Reproducing kernel function-based Filon and Levin methods for solving highly oscillatory integral

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  • Geng, F.Z.
  • Wu, X.Y.

Abstract

The main theme of this paper is to develop new Filon and Levin methods for highly oscillatory integrals. The novel method is based on the spline reproducing kernel functions approximation in Sobolev reproducing kernel Hilbert space. The accuracy and efficiency of the present method is illustrated through some numerical experiments compared with some effective methods appeared in the literature.

Suggested Citation

  • Geng, F.Z. & Wu, X.Y., 2021. "Reproducing kernel function-based Filon and Levin methods for solving highly oscillatory integral," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    • Handle: RePEc:eee:apmaco:v:397:y:2021:i:c:s009630032100028x
    DOI: 10.1016/j.amc.2021.125980
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    References listed on IDEAS

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    1. Andrzejczak, Grzegorz, 2018. "Spline reproducing kernels on R and error bounds for piecewise smooth LBV problems," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 27-44.
    2. Li, Xiuying & Li, Haixia & Wu, Boying, 2019. "Piecewise reproducing kernel method for linear impulsive delay differential equations with piecewise constant arguments," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 304-313.
    3. Ferreira, José Claudinei & Baquião, Maria Caruline, 2019. "A least square point of view to reproducing kernel methods to solve functional equations," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 206-221.
    4. Alvandi, Azizallah & Paripour, Mahmoud, 2019. "The combined reproducing kernel method and Taylor series for handling nonlinear Volterra integro-differential equations with derivative type kernel," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 151-160.
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