Issue |
Wuhan Univ. J. Nat. Sci.
Volume 27, Number 1, March 2022
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Page(s) | 26 - 34 | |
DOI | https://doi.org/10.1051/wujns/2022271026 | |
Published online | 16 March 2022 |
Mathematics
CLC number: O242.2
A Numerical Algorithm for Arbitrary Real-Order Hankel Transform
School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, Ningxia, China
† To whom correspondence should be addressed. E-mail: wws@nxu.edu.cn
Received: 5 November 2021
The Hankel transform is widely used to solve various engineering and physics problems, such as the representation of electromagnetic field components in the medium, the representation of dynamic stress intensity factors, vibration of axisymmetric infinite membrane and displacement intensity factors which all involve this type of integration. However, traditional numerical integration algorithms cannot be used due to the high oscillation characteristics of the Bessel function, so it is particularly important to propose a high precision and efficient numerical algorithm for calculating the integral of high oscillation. In this paper, the improved Gaver-Stehfest (G-S) inverse Laplace transform method for arbitrary real-order Bessel function integration is presented by using the asymptotic characteristics of the Bessel function and the accumulation of integration, and the optimized G-S coefficients are given. The effectiveness of the algorithm is verified by numerical examples. Compared with the linear transformation accelerated convergence algorithm, it shows that the G-S inverse Laplace transform method is suitable for arbitrary real order Hankel transform, and the time consumption is relatively stable and short, which provides a reliable calculation method for the study of electromagnetic mechanics, wave propagation, and fracture dynamics.
Key words: Hankel transform / large argument approximate expression of the Bessel function / linear transformation accelerated convergence algorithm (LTACA) / G-S inverse Laplace transform method (G-SILTM)
Biography: YANG Yonglin, male, Ph. D. candidate, research direction: singular integral equation and its application in new material mechanics. E-mail: yang_yongl@yeah.net
Foundation item: Supported by the National Natural Science Foundation of China (42064004, 12062022, 11762017, 11762016)
© Wuhan University 2022
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