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A Numerical Algorithm for Arbitrary Real-Order Hankel Transform

Authors :
Yonglin YANG
Xing LI
Shenghu DING
Wenshuai WANG
Source :
Wuhan University Journal of Natural Sciences. 27:26-34
Publication Year :
2022
Publisher :
EDP Sciences, 2022.

Abstract

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.

Subjects

Subjects :
Multidisciplinary

Details

ISSN :
19934998 and 10071202
Volume :
27
Database :
OpenAIRE
Journal :
Wuhan University Journal of Natural Sciences
Accession number :
edsair.doi...........ee3e467363e22cd96cbd3c16e3435502
Full Text :
https://doi.org/10.1051/wujns/2022271026