Coşkun DENİZ


Determination of zeros of Bessel functions and their derivatives are essential in the TE and TM modes supported by the circular waveguides. However, since these functions are conventionally defined as infinite series, fast calculation of their numerical values and zeros with reliable accuracy requires improved numerical techniques or approximations. Moreover, modes are usually sorted by human inspection and instant retrieval of correctly ordered modes becomes essential especially for higher mode-index values. Here, a fast computational algorithm design based on the numerical Bisection method to determine the sorted TE and TM mode solutions of the circular waveguides is presented. Our suggestion involves: i) determination of the critical points close to the zeros of Bessel functions and their derivatives within the user selected sampling width (typically =0.01), ii) application of the numerical Bisection method to these functions one after another to scan up to the user selected maximum index number by using these critical points up to maintain the user selected sensitivity values, iii) Bubble sorting of the unified roots matrix, iv) scan the bubble sorted roots matrix to decide the mode type. As a result, our design finds the related TE and TM modes along with the cut-off and propagating wave frequencies in the correct order with a very fast calculation by the user controlled Computable Document File (CDF) environment.

Anahtar Kelimeler

Bessel functions, circular waveguides, cylindrical waveguides, TE modes, TM modes, Computable Document File (CDF), real time computation

Tam Metin:

PDF (English)


Abramowitz A. and Stegun I.A., 1965, Handbook of mathematical functions, with formulas, Graphs, and Mathematical Tables, 3rd printing with corrections, Vol. 55 of NBS Applied mathematics series, superintendent of documents, US Government Printing Office, Washington DC, pp. 355—479.

Abuelma’atti, M. T., 1999, “Trigonometric approximations for some Bessel functions”, Active and Passive Elec. Comp., Vol. 22, pp. 75-85.

Arfken H.J. and Weber, G.B., 2005, Mathematical methods for physicists (6th ed.), Elsevier Academic Press, pp. 675—686.

Arora, N., Kumar, S., and Tamta, V.K., 2012, “A novel sorting algorithm and comparison with Bubble sort and Insertion sort”, International Journal of Computer Applications, Vol. 45(1): pp. 31—32.

Astrachan, O., 2003, “Bubble Sort: An archaeological algorithmic analysis”, SIGCSE '03 Proceedings of the 34th SIGCSE Technical Symposium on Computer Science Education, NY, pp. 1—5.

Balanis, C., 1989, Advanced Engineering Electromagnetics (2nd ed.), Wiley, NY, pp. 483—500.

Beattie, C. L., 1958, Table of first 700 zeros of Bessel functions—Jl(x) and Jl’(x), Bell System Technical Journal, 37, pp. 689—697.

Bell, W.W., 1968, Special functions for scientists and engineers, D. Van Nostrand Compant Ltd., London, pp. 92—110.

Blachman, N. M. and Mousavinezhad, S. H., 1986, “Trigonometric approximations for Bessel functions”, EEE Transactions on Aerospace and Electronic Systems, Vol. AES-22(1): 2—7.

Boas, L.M., 2006, Mathematical methods in the physical sciences (3rd ed.), Wiley, NY, pp. 587—606.

Chapra, S. and Canale, R., 2014, Numerical methods for engineers (7th ed.), WCB/McGraw-Hill, NY, pp. 148—154.

Cheng, D. K., 1989, Field and wave electromagnetics (2nd ed.), Addison-Wesley, London, pp., 562—572.

Cormen, T. H., Leiserson, C. E., Rivest, R. L., and Stein, C., 2009, Introduction to algorithms (3rd ed.), MIT Press, USA, p. 40.

Deniz, C., 2017, “A Newton Raphson Based Roots Finding Algorithm Design and its Applications to Circular Waveguides”, El-Cezeri Journal of Science and Engineering, Vol. 4(1), pp. 32—45

Hamming, R. W., 1987, Numerical methods for scientists and engineers (2nd Revised ed., Dover Books on Mathematics), Dover Publications, NY, pp. 68—72.

Harrison, J., 2009, “Fast and accurate Bessel function computation”, Computer Arithmetic-proc. of 19th EEE symp. on Computer Arithmetic, Portland-Oregon, pp. 104—113.

Hoffman, J.D., 2001, Numerical methods for engineers and scientists (2nd ed.), Marcel Dekkel, NY-Basel, pp. 141—154.

Khairullah, Md., 2013, “Enhancing worst sorting algorithms, International Journal of Advanced Science and Technology”, Vol. 56, pp. 13—26.

Korenev, B.G., 2002, Bessel functions and their applications, Taylor and Francis, NY.

Luke, Y. L., 1975, Approximation of special Functions, Academic Press, NY.

Millane R. P. and Eads, J. L., 2003, “Polynomial approximations to Bessel functions”, IEEE Transactions On Antennas And Propagation, 51(6), pp. 1398—1400.

Newman, J. N., 1984, “Approximations for the Bessel and Struve functions”, Mathematics of Computation, Vol. 43(168), pp. 551—556.

Richards, D., 2002, Advanced mathematical methods with maple, Cambridge University Press, UK, pp. 325—331.

Rohil, H. and Manisha, 2014, “Run time Bubble sort–An enhancement of Bubble sort”, International Journal of Computer Trends and Technology (IJCTT), Vol. 14(1), pp. 36—38.

Sekeljic, N., 2010, “Asymptotic expansion of Bessel functions; applications to electromagnetics”, Dynamics at the Horsetooth, Focused Issue: Asymptotics and Perturbations, Vol. 2A, pp. 1—11.

Waldron, R.A., 1981, Formulas for computation of approximate values of some Bessel functions, Proceedings of the IEEE, 69, pp. 1686-1588.

Watson, G.N., 1995, A treatise on the theory of Bessel functions (2nd ed.), Cambridge University Press, NY.

Wolfram, S., 2003, The Mathematica Book (5th ed.), Wolfram Media Inc., 5th edition, USA, pp. 29—35&pp. 102—110.

WIKIPEDIA, 2017a, Computable Document Format, https://en.wikipedia.org/wiki/Computable_Document_Format (accessed in 2017)

WIKIPEDIA, 2017b, Bubble Sort, https://en.wikipedia.org/wiki/Bubble_sort (accessed in 2017).

WOLFRAM, 2017a, Wolfram Documentation Center, BesselJ, http://reference.wolfram.com/mathematica/ref/BesselJ.html (accessed in 2017).

WOLFRAM, 2017b, Wolfram CDF player, https://www.wolfram.com/cdf-player/ (accessed in 2017).

WOLFRAM, 2017c, Computable Document Format, http://www.wolfram.com/events/siam-2016/files/CDF-4.pdf (accessed in 2017).

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