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.
Great job. But it fails to find the first roots when you use bessel of the second kind. for example if i want the zeros of the order 2 second kind,
This algorithm gives
whereas the correct values should have been
Haven't tested second kind functions though
Utilizei a rotina para calcular a solução analítica da equação da difusão 2D. Ficou muito boa.
what are the advantages of using this over fzero? thanks
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.
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
i dont have comments jeje sorry but this informaion is good ! ! thank you!!!
Thank you, very useful
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.
It works just fine
j'ai male a trouver la solution de l'equation dde la gaine fini et infini de la fibre vouler vous m'aider svp.
Nice work. You've saved me a lot of time.
Good -- more commenting / discussion would be nice.
I am using it. But not sure about its accuracy.
Very good. Works perfectly.
BGU University Israel
French student thank you.
We hope you'll have a good life.
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.
It seems the besselzero(n,k,1) and besselzero(n,k,2) works fine. Checked with multiple plot(besselzero(n,100,kind)).
Good work ...
The guess function has been improved so the script is more robust. Also I have added bessel functions of the second kind.