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An Efficient Quadrature Rule for the Oscillatory Infinite Generalized Bessel Transform with a General Oscillator and Its Error Analysis

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Abstract

Our recent work (Kang and Wang in J Sci Comput 82:1–33, 2020) performed a complete asymptotic analysis and proposed a modified Filon-type method for a class of oscillatory infinite Bessel transform with a general oscillator. In this paper, we present and analyze a different method by converting the integration path to the complex plane for this class of oscillatory infinite Bessel transform. In particular, we establish a series of new quadrature rules for this transform and carry out rigorous analysis, including the cases that the oscillator g(x) has either zeros or stationary points. The error analysis shows the advantages that this approach exhibits high asymptotic order, and the accuracy improves significantly as either the frequency \(\omega \) or the number of nodes n increases. Furthermore, the constructed method shows higher accuracy and error order by comparing with the existing modified Filon-type method in our recent work (Kang and Wang 2020) at the same computational cost. Some numerical experiments are provided to verify the theoretical results and demonstrate the efficiency of the proposed method.

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All data generated or analyzed during this study are included in this article. The codes required during the algorithm implementation are available from the corresponding author on reasonable request.

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Acknowledgements

The first author was supported by Zhejiang Provincial Natural Science Foundation of China under Grant Nos. LY22A010002, LY18A010009, National Natural Science Foundation of China (Grant Nos. 11301125, 11971138) and Research Foundation of Hangzhou Dianzi University (Grant No. KYS075613017). The second author was supported by Graduate Students’ Excellent Dissertation Cultivation Foundation of Hangzhou Dianzi University (Grant No. GK208802299013-110). The authors would like to express their most sincere thanks to the referees and editors for their very helpful comments and suggestions, which greatly improved the quality of this paper.

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  1. Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, 310018, Zhejiang, People’s Republic of China

    Hongchao Kang & Hong Wang

  2. School of Mathematics and Statistics, Central South University, Changsha, 410083, Hunan, People’s Republic of China

    Hong Wang

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  1. Hongchao Kang
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Correspondence to Hongchao Kang.

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The first author was supported by Zhejiang Provincial Natural Science Foundation of China under Grant Nos. LY22A010002, LY18A010009, National Natural Science Foundation of China (Grant Nos. 11301125, 11971138) and Research Foundation of Hangzhou Dianzi University (Grant No. KYS075613017). The second author was supported by Graduate Students’ Excellent Dissertation Cultivation Foundation of Hangzhou Dianzi University (Grant No. GK208802299013-110).

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Kang, H., Wang, H. An Efficient Quadrature Rule for the Oscillatory Infinite Generalized Bessel Transform with a General Oscillator and Its Error Analysis. J Sci Comput 94, 29 (2023). https://doi.org/10.1007/s10915-022-02081-6

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  • DOI: https://doi.org/10.1007/s10915-022-02081-6

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