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Bessel Function Zeros

25 Jan 2005 (Updated 27 Jan 2005)

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

File Information
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.
MATLAB release	MATLAB 7 (R14)

Tags for This File
Everyone's Tags	1, 1 and it is different than the mathematica besselyzero12, 2, bessel functions(2), first, halleys method, i am using r2008a and the command is besselzero12, i tried to compute y12, rootfinding, second, zeros
Tags I've Applied
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Comments and Ratings (19)
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 ...
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.
05 Dec 2005	PinceDor Ema	French student thank you. We hope you'll have a good life.
20 Apr 2006	Hung Lin
11 Jul 2006	T S	Very good. Works perfectly. Thanks T.S BGU University Israel
18 Aug 2006	Jim Morehead
13 Oct 2006	Kathirvel Thiyagarajan	I am using it. But not sure about its accuracy.
15 Nov 2006	R Parthasarathy	Good -- more commenting / discussion would be nice.
26 Nov 2006	Bryan Romero	works great
20 Mar 2007	Warren Parsons	Nice work. You've saved me a lot of time.
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.
01 May 2007	Michele Campisi	It works just fine
05 May 2007	ionel aurel
02 Oct 2007	miguel m
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 Mar 2008	Yaniv Shaposhnik	Thank you, very useful
08 Oct 2008	Jesús Aurelio	i dont have comments jeje sorry but this informaion is good ! ! thank you!!!
22 Feb 2009	ZeRO LiFT	Good luck
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

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Updates
27 Jan 2005	The guess function has been improved so the script is more robust. Also I have added bessel functions of the second kind.

Tag Activity for this File
Tag	Applied By	Date/Time
zeros	Greg von Winckel	22 Oct 2008 07:40:13
bessel functions	Greg von Winckel	22 Oct 2008 07:40:13
first	Greg von Winckel	22 Oct 2008 07:40:13
second	Greg von Winckel	22 Oct 2008 07:40:13
rootfinding	Greg von Winckel	22 Oct 2008 07:40:13
halleys method	Greg von Winckel	22 Oct 2008 07:40:13
i tried to compute y12	Baris Avsaroglu	24 Jul 2009 16:40:22
1 and it is different than the mathematica besselyzero12	Baris Avsaroglu	24 Jul 2009 16:40:23
1	Baris Avsaroglu	24 Jul 2009 16:40:23
2	Baris Avsaroglu	24 Jul 2009 16:41:27
i am using r2008a and the command is besselzero12	Baris Avsaroglu	24 Jul 2009 16:41:27
bessel functions	Baris Avsaroglu	24 Jul 2009 16:42:30

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