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

Longbin Zhao, Pengde Wang and Qiongqi Fan

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 228, issue C, 202-210

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.

Keywords: Quadrature method; Oscillatory Bessel kernel; Moment-free; Convergence; Asymptotic order (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:228:y:2025:i:c:p:202-210

DOI: 10.1016/j.matcom.2024.09.002

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