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Exponential fitting collocation methods for a class of Volterra integral equations

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  • Zhao, Longbin
  • Huang, Chengming

Abstract

In this paper, we propose a collocation method for a class of Volterra integral equations whose solutions contain periodic functions. Since the exponential fitting interpolation has an advantage in approximating periodic functions, we consider employing it with collocation method to construct our scheme. The global convergence analysis of the scheme is also presented based on the interpolation error. The theoretical results, as well as the superiority of the method, are verified in the numerical part.

Suggested Citation

  • Zhao, Longbin & Huang, Chengming, 2020. "Exponential fitting collocation methods for a class of Volterra integral equations," Applied Mathematics and Computation, Elsevier, vol. 376(C).
    • Handle: RePEc:eee:apmaco:v:376:y:2020:i:c:s0096300320300904
    DOI: 10.1016/j.amc.2020.125121
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    References listed on IDEAS

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    1. Wen, Liping & Yu, Yuexin, 2016. "Convergence of Runge–Kutta methods for neutral delay integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 84-96.
    2. Cardone, A. & Ixaru, L.Gr. & Paternoster, B. & Santomauro, G., 2015. "Ef-Gaussian direct quadrature methods for Volterra integral equations with periodic solution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 110(C), pages 125-143.
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    Cited by:

    1. Zhao, Longbin & Wang, Pengde, 2022. "Error estimates of piecewise Hermite collocation method for highly oscillatory Volterra integral equation with Bessel kernel," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 137-150.

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