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Solving Bessel differential equation of order zero using exponentially fitted collocation approximation method

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Author Affiliations

  • 1Department of Mathematics, Faculty of Computing and Mathematical Sciences, Kano University of Science and Technology, P.M.B 3244 Wudil Kano State, Nigeria
  • 2Department of Mathematics, Faculty of Computing and Mathematical Sciences, Kano University of Science and Technology, P.M.B 3244 Wudil Kano State, Nigeria

Res. J. Mathematical & Statistical Sci., Volume 7, Issue (2), Pages 21-26, May,12 (2019)

Abstract

This paper presents analytic-numeric solution Bessel differential equations of order zero using Exponentially Fitted Collocation Approximation Method (EFCAM). This technique was employed to obtain the analytic-numerical solutions of Bessel equations. The method introduces a significant improvement in solving differential equations on mathematical physics. The numerical results obtained by EFCAM are in good agreement with exact solution and available results in literature with little error and showed effectiveness of the proposed method.

References

  1. Curtis W. (2018)., On the Early History of Bessel Functions on JSTOR 1-4., www.jstor.org
  2. Wu J.H., Liu A.Q. and Chen H.L. (2007)., Exact solutions for free-vibration analysis of rectangular plates using Bessel functions., Journal of Applied Mechanics, 74(6), 1247-1251.
  3. Korenev B.G. (2003)., Bessel Functions and Their Applications., CRC Press, 23-26.
  4. Davies Brian (2001)., Integral Transforms and Their Applications., Third Edition. Springer 14-16.
  5. Bowman F. (1958)., Introduction to Bessel Functions., Dover New York.
  6. Gray A., Mathews G.B. and MacRobert T.M. (1953)., A Treatise on Bessel Functions., Basingstoke MacMillan.
  7. McLachlan N.W. (1955)., Bessel Functions for Engineers., 2nd Edition, Oxford University Press, London.
  8. Falade K.I. (2015)., Exponentially fitted collocation approximation method for singular initial value problems and integro-differential equations., (unpublished doctoral thesis), University of Ilorin, Ilorin Nigeria.
  9. Breuer K.S. and Everson R.M. (1992)., On the errors incurred calculating derivatives using Chebyshev polynomials., Journal of Computational Physics, 99(1), 56-67.
  10. Taiwo O.A. and Olagunju A.S. (2012)., Chebyshev methods for the numerical solution of fourth-order differential equations., International Journal of Physical Sciences, 7(13), 2032-2037.
  11. Shiralashetti S. and Deshi A. (2017)., Chebyshev Wavelet Collocation Method for the Numerical Solution of Ordinary Differential Equations., Journal of the Nigerian Mathematical Society, 36(2), 337-353. www.nigerianmathematicalsociety.org
  12. Entisar A.S. and Magdi E.I. (2016)., Solution of Bessel Differential Equation of order Zero by Using Different Methods in Critical Study., International Journal of Engineering Sciences & Management, 6(1), 35-38. https://www.researchgate.net/publication/297733694.