Fast algorithms and analysis of oscillatory and weakly singular generalized Bessel transforms

Hongchao Kang, Chunzhi Xiang, Guidong Liu, Ao Liu and Xinrui Hou

Applied Mathematics and Computation, 2025, vol. 490, issue C

Abstract: In this paper we investigate the calculation and analysis for a class of the highly oscillatory generalized Bessel transform with endpoint singularities of algebraic type. First, when the oscillator has either zeros or stationary points, we give many asymptotic expansions for the transform. On the basis of these results, we construct a new and good modified Filon-type method. Moreover, based on the resulting asymptotic expansions we can perform the error analysis in inverse powers of ω. In addition, the proposed methods share the property that the precision improves greatly, for fixed multiplicities and number of nodes, as ω increases. Our theoretical analysis can be verified by some numerical examples. Finally, by numerical comparison we can see that the accuracy of the proposed modified Filon-type methods is much higher than those of the existing Filon method and the method proposed by Tripathi etc. in 2014 at the same computational cost.

Keywords: Singularity; Oscillatory Bessel transform; Critical points; Asymptotic analysis; Error estimate; New and efficient numerical method (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:490:y:2025:i:c:s0096300324006672

DOI: 10.1016/j.amc.2024.129206

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