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A quadrature method for Volterra integral equations with highly oscillatory Bessel kernel

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  • Zhao, Longbin
  • Wang, Pengde
  • Fan, Qiongqi

Abstract

To avoid computing moments, this work adopts generalized quadrature method for Volterra integral equations with highly oscillatory Bessel kernel. At first, we study the influence of the interval length and frequency in detail after recalling the construction of the quadrature method. Then, the two-point quadrature method is employed for the equation. By estimating the weights, we could guarantee that the discretized equation is solvable. For its convergence, our analysis shows that the proposed method enjoys asymptotic order 5/2 and as h decreases it converges with order 2 as well. Some numerical illustrations are provided to test the method in the numerical part.

Suggested Citation

  • Zhao, Longbin & Wang, Pengde & Fan, Qiongqi, 2025. "A quadrature method for Volterra integral equations with highly oscillatory Bessel kernel," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 228(C), pages 202-210.
    • Handle: RePEc:eee:matcom:v:228:y:2025:i:c:p:202-210
    DOI: 10.1016/j.matcom.2024.09.002
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    References listed on IDEAS

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    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.
    2. Fang, Chunhua & Ma, Junjie & Xiang, Meiying, 2015. "On Filon methods for a class of Volterra integral equations with highly oscillatory Bessel kernels," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 783-792.
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