Bessel Function Zeros

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

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 submission has inspired the following:; ZEROBESS
• MATLAB release: MATLAB 7 (R14)

[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 ...

[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.

[PinceDor Ema]

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

[Hung Lin]

 

[T S]

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

[Jim Morehead]

 

[Kathirvel Thiyagarajan]

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

[R Parthasarathy]

Good -- more commenting / discussion would be nice.

[Bryan Romero]

works great

[Warren Parsons]

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

[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.

[Michele Campisi]

It works just fine

[ionel aurel]

 

[miguel m]

 

[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.

[Yaniv Shaposhnik]

Thank you, very useful

[Jesús Aurelio]

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

[ZerO]

Good luck

[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

[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.

[Lube F]

what are the advantages of using this over fzero? thanks