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Bessel Function Zeros

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25 Jan 2005 (Updated )

Computes the first k zeros of the Bessel Function of the 1st and 2nd Kinds.

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Description

This script uses Halley's method to compute the positive k zeros of the Bessel function of the first kind J(n,x) and second kind Y(n,x) where n is a positive number. The routine has been tested for up to k=100 and n=100.

Acknowledgements

This file inspired Zerobess and Bessel Zero Solver.

MATLAB release MATLAB 7 (R14)
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Comments and Ratings (21)
14 Jul 2012 Roberto Pettres

Utilizei a rotina para calcular a solução analítica da equação da difusão 2D. Ficou muito boa.

01 Mar 2010 Lube F

what are the advantages of using this over fzero? thanks

02 Feb 2010 Timothy

Mostly seems to work. However, the zeros for the Bessel functions of the second kind are missing the first zero (0.893576966279). That is, the first Y_n zero it gives is actually the second, the second is actually the third, and so on.

24 Jul 2009 Baris Avsaroglu

Hi all

I am using the function in Matlab R2008a
I entered the command besselzero(1/2,1,2)
and the result is different than the value from
Mathematica s BesselYZero[1/2,1]
I also tried some other combinations which seemed fine.
I just wonder if this is a special case or I should check
the numbers given by this Matlab function with some other online sources. Thanks

08 Oct 2008 Jesús Aurelio

i dont have comments jeje sorry but this informaion is good ! ! thank you!!!

02 Mar 2008 Yaniv Shaposhnik

Thank you, very useful

29 Jan 2008 Farshid Ghassemi

The algorithm is fascinating and the speed is satisfactory. But there is a small defect: For Y function, the initial guess is not correctly chosen and the routine misses the first root in some cases.

02 Oct 2007 miguel m  
05 May 2007 ionel aurel  
01 May 2007 Michele Campisi

It works just fine

23 Apr 2007 harrouni lyes

j'ai male a trouver la solution de l'equation dde la gaine fini et infini de la fibre vouler vous m'aider svp.

20 Mar 2007 Warren Parsons

Nice work. You've saved me a lot of time.

26 Nov 2006 Bryan Romero

works great

15 Nov 2006 R Parthasarathy

Good -- more commenting / discussion would be nice.

13 Oct 2006 Kathirvel Thiyagarajan

I am using it. But not sure about its accuracy.

18 Aug 2006 Jim Morehead  
11 Jul 2006 T S

Very good. Works perfectly.
Thanks
T.S
BGU University Israel

20 Apr 2006 Hung Lin  
05 Dec 2005 PinceDor Ema

French student thank you.
We hope you'll have a good life.

03 Dec 2005 Joey Pittman

I used this m-file to generate the zeros for a bessel function of the first kind and order zero and it worked just fine.

When you run the function, you should use besselzero(n,k,kind) I interpreted the documentation to suggest that the function needs only 2 inputs, but it really requires 3 to work.

04 Aug 2005 Stepan Matejka

It seems the besselzero(n,k,1) and besselzero(n,k,2) works fine. Checked with multiple plot(besselzero(n,100,kind)).
Good work ...

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