Open Access
Issue |
Wuhan Univ. J. Nat. Sci.
Volume 27, Number 1, March 2022
|
|
---|---|---|
Page(s) | 26 - 34 | |
DOI | https://doi.org/10.1051/wujns/2022271026 | |
Published online | 16 March 2022 |
- Kaufman A A, Keller G V. Frequency and Transient Soundings [M]. Beijing: Geological Publishing House, 1987. [Google Scholar]
- Fang W Z, Li Y G, Li X. Theory of TEM Sounding [M]. Xian: Press of North-west Industry University, 1993(Ch). [Google Scholar]
- Wen A H, Wang X Q. Utilizing direct integration to enhance calculation accuracy of 1D electromagnetic response for current dipole source [J]. Northwestern Seismological Journal, 2003, 25(3): 193-197(Ch). [Google Scholar]
- Ji G, Zhang W K, Lu X P. Numerical integration on Green source function with free water surface [J]. Journal of Naval University of Engineering, 2004, 16(6): 89-92(Ch). [Google Scholar]
- He J S, Bao L Z. EM field of vertical wire electric source and its practical meaning [J]. Journal of Central South University (Science and Technology), 2011, 42(1): 130-135(Ch). [Google Scholar]
- Singh B M, Rokne J, Dhaliwal R S. Diffraction of antiplane shear waves by a finite crack in a piezoelectric material [J]. ZAMM-Journal of Applied Mathematics and Mechanics /Zeitschrift Für Angewandte Mathematik Und Mechanik, 2011, 91(11): 866-874. [CrossRef] [MathSciNet] [Google Scholar]
- Yang Y L, Li X, Wang W S. Wettability of semispherical droplets on layered elastic gradient soft substrates [J]. Scientific Reports, 2021, 11(1): 2236. [NASA ADS] [CrossRef] [PubMed] [Google Scholar]
- Zhang Q A, Wu F T, Zheng W T, et al. Self-reconstructing properties of high-order Besssel-Gauss beam [J]. Scientia Sinica Physica, Mechanica & Astronomica, 2011, 41(10): 1131-1137. [NASA ADS] [CrossRef] [Google Scholar]
- You K M, Lin Y L, Wang Y W, et al. High order Hankel transform based on Dini expansion and its applications in beam propagation [J]. Acta Physica Sinica, 2013, 62(14): 30-35. [Google Scholar]
- Wang W J. Propagation of the Bessel Gaussian Beam in Turbulence and Application [D]. Xi’an: Xidian University, 2019(Ch). [Google Scholar]
- Meng X S. Electromagnetic Vortex Wave Generation and Target Near-Field Scattering Based on Artificial Electromagnetic Metasurface [D]. Xi’an: Xidian University, 2019(Ch). [Google Scholar]
- Blakemore M, Evans G, Hyslop J. Comparison of some methods for evaluating infinite range oscillatory integrals [J]. Journal of Computational Physics, 1976, 22(3): 352-376. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
- Chave A D. Numerical integration of related Hankel transforms by quadrature and continued fraction expansion [J]. Geophysics, 1983, 48(12): 1671-1686. [NASA ADS] [CrossRef] [Google Scholar]
- Cree M J, Bones P J. Algorithms to numerically evaluate the Hankel transform [J]. Computers & Mathematics with Applications, 1993, 26(1): 1-12. [CrossRef] [MathSciNet] [Google Scholar]
- Lucas S K, Stone H A. Evaluating infinite integrals involving Bessel functions of arbitrary order [J]. Journal of Computational and Applied Mathematics, 1995, 64(3): 217-231. [CrossRef] [MathSciNet] [Google Scholar]
- Guptasarma D, Singh B. New digital linear filters for Hankel J0 and J1 transforms [J]. Geophysical Prospecting, 1997, 45(5): 745-762. [CrossRef] [Google Scholar]
- Filon L N G. On a quadrature formula trigonometric integrals [J]. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 1928, 49: 38-47. [Google Scholar]
- Yu R. Two Types of Bessel Transform Its Numerical Integration Methods [D]. Changsha: Central South University, 2007(Ch). [Google Scholar]
- Chen R Y. Numerical analysis on a class of integrals involving Bessel function [J]. Journal of Chongqing Institute of Technology (Natural Science), 2008, 22(11): 83-88(Ch). [Google Scholar]
- Chen R Y. Numerical approximations to integrals with a highly oscillatory Bessel kernel [J]. Applied Numerical Mathematics, 2012, 62(5): 636-648(Ch). [CrossRef] [MathSciNet] [Google Scholar]
- Zhang H Q, Chen Y, Nie X. Fast Hankel transforms algorithm based on kernel function interpolation with exponential functions [J]. Journal of Applied Mathematics, 2014, 2014: 1-7. [Google Scholar]
- Niu F F. A Numerical Method for Computing Highly Oscillatory Integrals with a Bessel Kernel [D]. Wuhan: Huazhong University of Science &Technology, 2015(Ch). [Google Scholar]
- Majidian H. Numerical approximation of highly oscillatory integrals on semi-finite intervals by steepest descent method [J]. Numerical Algorithms, 2012, 63(3): 537-548. [Google Scholar]
- Cohen H, Villegas F R, Zagier D. Convergence acceleration of alternating series [J]. Experimental Mathematics, 2000, 9(1): 3-12. [CrossRef] [MathSciNet] [Google Scholar]
- Wang H J, Li G. Hankel transform to accelerate the convergence of the numerical integration algorithm [J]. Technological Development of Enterprise, 2012, 31(16): 8-9+44(Ch). [Google Scholar]
- Gao J Z, Chen R Y. On computation of high frequency Hankel transforms [J]. Alexandria Engineering Journal, 2019, 58(3): 1033-1037. [CrossRef] [Google Scholar]
- Kisselev A V. Exact expansions of Hankel transforms and related integrals [J]. The Ramanujan Journal, 2020, 55: 349-367. [Google Scholar]
- Raiche A P. Transient electromagnetic field computations for polygonal loops on layered earth [J]. Geophysics, 1987, 526: 785-793. [NASA ADS] [CrossRef] [Google Scholar]
- Villinger H. Solving cylindrical geothermal problems using Gaver-Stehfest inverse Laplace transform [J]. Geophysics, 1985, 50(10): 1581-1587. [NASA ADS] [CrossRef] [Google Scholar]
- Li D Z, Yang Z Q, Liang Z. Numerical computation of Bessel function for complex arguments [J]. Journal of University of Electronic Science and Technology of China, 1996, 25(7): 125-128(Ch). [Google Scholar]
- Hua J, Jiang Y S, Wang W B. The numerical integration of dual Hankel transformation [J]. Coalgeology and Exploration, 2001, 29(3): 58-62. [Google Scholar]
- Zeidler E. Teubner-Taschenbuch der Mathematik [M]. Berlin: Vieweg+Teubner Verlag, 2012. [Google Scholar]
- Luo H G. The Study about 1D Forward Modeling of Large-Fixed Loop TEM [D]. Beijing:China University of Geosciences (Beijing), 2012(Ch) . [Google Scholar]
- Anderson W L. Fast Hankel transforms using related and lagged convolutions [J]. ACM Transactions on Mathematical Software, 1982, 8(4): 344-368. [CrossRef] [Google Scholar]
- Kasemsuwan J, Sabau S V, Somboon U. Differential transformation method for circular membrane vibrations [J]. Bulletin of the Transilvania University of Brasov, Series III: Mathematics, Informatics, Physics, 2020, 61(12): 333-350 [CrossRef] [Google Scholar]
- Gradshteyn I S, Ryzhik I M. Table of Integrals, Series, and Products [M]. Seventh Edition. Amsterdam: Elsevier, 2007: 743. [MathSciNet] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.