On the computation of zeros of Bessel functions
Keywords:
Bessel functions, Zeros, Bisection Method
Abstract
The zeros of some chosen Bessel functions of different orders is revised using the well-known bisection method , McMahon formula is also reviewed and the calculation of some zeros are carried out implementing a recent version of MATLAB software.
The obtained results are analyzed and discussed on the lights of previous calculations.
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References
[1] Akrim , M.S.(2015) Bessel Functions and Bessel-Fourier series in Boundary-value Problems , MSc Thesis , University of Tripoli , Tripoli .
[2] Arfken , G.(1970) Mathematical Methods for Physicits , 2^nd Edition , Academic Press , New York.
[3] Awin , A.M. (2003) Lectures on Mathematical Methods , 1^st Edition , Dar Alkitaab Aljadeed , Beirut.
[4] Grad , J. , Zakrajseh , E. (1973) Method for Evaluation of Zeros of Bessel Functions , Journal of the Institute of Mathematics and its Applications , 11 , 57-72.
[5] Ikebe , Y. , Kikuehi , Y. , Fujishiro, I. (1991) Computing Zeros and Orders of Bessel Functions , Journal of Computational and Applied Mathematics , 38 , 169-184.
[6] Elbert , A. (2001)Some Recent Results on the zeros of Bessel Functions and Orthogonal Polynomials , Journal of Computational and Applied Mathematics , 133 , 65-83.
[7] Nicholson , J. (2018) Bessel Zero Solver , MATLAB Version 1.1 (31.7 kB)(R 20146)
https://www.mathworks.com/matlabcentral/fileex change/48403_bessel_zero_solver
[8] Awin , A.M. (2010) Numerical Methods , 1^st Edition , Misurata University Publishing , Misurata .
[9] Watson , G.N. (1944) A Treatise of the Theory of Bessel Functions , 2^nd Edition , Cambridge University Press , Cambridge .
[10] Olver , F.W.J. (1951) A Further Method for the Evaluation of Zeros of Bessel Functions and Some New Asymptotic Expansions for Zeros of Functions of large Order , Mathematical Proceedings of the Cambridge Philosophical Society , 47 , 699-712
[11] Kerimov , M.K. (2014) Studies on the Zeros of Bessel Functions and Methods for their Computation , Computational Mathematics and Mathematical Physics ,
54(9) , 1337-1388 .
[12] Kerimov , M.K. (2016) Studies on the Zeros of Bessel Functions and Methods for their Computation : 2. Monotonicity , Convexity , Concavity , and other Properties , Computational Mathematics and Mathematical Physics , 56(7) , 1175-1208.
DOI : 10.1134/50965542516070095
[13] Kerimov , M.K. (2016) Studies on the Zeros of Bessel Functions and Methods for their Computation : 3. Some New Works on Monotonicity , Convexity , and Other Properties , Computational Mathematics and Mathematical Physics , 56(12) , 1949-1991.
[14] Kerimov , M.K. (2018) Studies on the Zeros of Bessel Functions and Methods for their Computation :IV. Inequalities , Estimates , Expansions…etc.for Zeros of Bessel Functions , Computational Mathematics and Mathematical Physics , 58 , 1-37.
[2] Arfken , G.(1970) Mathematical Methods for Physicits , 2^nd Edition , Academic Press , New York.
[3] Awin , A.M. (2003) Lectures on Mathematical Methods , 1^st Edition , Dar Alkitaab Aljadeed , Beirut.
[4] Grad , J. , Zakrajseh , E. (1973) Method for Evaluation of Zeros of Bessel Functions , Journal of the Institute of Mathematics and its Applications , 11 , 57-72.
[5] Ikebe , Y. , Kikuehi , Y. , Fujishiro, I. (1991) Computing Zeros and Orders of Bessel Functions , Journal of Computational and Applied Mathematics , 38 , 169-184.
[6] Elbert , A. (2001)Some Recent Results on the zeros of Bessel Functions and Orthogonal Polynomials , Journal of Computational and Applied Mathematics , 133 , 65-83.
[7] Nicholson , J. (2018) Bessel Zero Solver , MATLAB Version 1.1 (31.7 kB)(R 20146)
https://www.mathworks.com/matlabcentral/fileex change/48403_bessel_zero_solver
[8] Awin , A.M. (2010) Numerical Methods , 1^st Edition , Misurata University Publishing , Misurata .
[9] Watson , G.N. (1944) A Treatise of the Theory of Bessel Functions , 2^nd Edition , Cambridge University Press , Cambridge .
[10] Olver , F.W.J. (1951) A Further Method for the Evaluation of Zeros of Bessel Functions and Some New Asymptotic Expansions for Zeros of Functions of large Order , Mathematical Proceedings of the Cambridge Philosophical Society , 47 , 699-712
[11] Kerimov , M.K. (2014) Studies on the Zeros of Bessel Functions and Methods for their Computation , Computational Mathematics and Mathematical Physics ,
54(9) , 1337-1388 .
[12] Kerimov , M.K. (2016) Studies on the Zeros of Bessel Functions and Methods for their Computation : 2. Monotonicity , Convexity , Concavity , and other Properties , Computational Mathematics and Mathematical Physics , 56(7) , 1175-1208.
DOI : 10.1134/50965542516070095
[13] Kerimov , M.K. (2016) Studies on the Zeros of Bessel Functions and Methods for their Computation : 3. Some New Works on Monotonicity , Convexity , and Other Properties , Computational Mathematics and Mathematical Physics , 56(12) , 1949-1991.
[14] Kerimov , M.K. (2018) Studies on the Zeros of Bessel Functions and Methods for their Computation :IV. Inequalities , Estimates , Expansions…etc.for Zeros of Bessel Functions , Computational Mathematics and Mathematical Physics , 58 , 1-37.
Published
2023-01-12
How to Cite
Ahmed, T. E., Akrim, M. S., Abdeen, K. S., & Awin, A. M. (2023). On the computation of zeros of Bessel functions. Journal of Progressive Research in Mathematics, 20(1), 1-15. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/2171
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