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

Author

Listed:
  • Kang, Hongchao
  • Xiang, Chunzhi
  • Liu, Guidong
  • Liu, Ao
  • Hou, Xinrui

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.

Suggested Citation

  • Kang, Hongchao & Xiang, Chunzhi & Liu, Guidong & Liu, Ao & Hou, Xinrui, 2025. "Fast algorithms and analysis of oscillatory and weakly singular generalized Bessel transforms," Applied Mathematics and Computation, Elsevier, vol. 490(C).
    • Handle: RePEc:eee:apmaco:v:490:y:2025:i:c:s0096300324006672
    DOI: 10.1016/j.amc.2024.129206
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    References listed on IDEAS

    as
    1. Wang, Hong & Kang, Hongchao & Ma, Junjie, 2024. "An efficient and accurate numerical method for the Bessel transform with an irregular oscillator and its error analysis," Applied Mathematics and Computation, Elsevier, vol. 473(C).
    2. Xu, Zhenhua & Milovanović, Gradimir V. & Xiang, Shuhuang, 2015. "Efficient computation of highly oscillatory integrals with Hankel kernel," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 312-322.
    3. Manoj P. Tripathi & B. P. Singh & Om P. Singh, 2014. "Stable Numerical Evaluation of Finite Hankel Transforms and Their Application," International Journal of Analysis, Hindawi, vol. 2014, pages 1-11, November.
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