Bessel Derivative Zeros

Zeros of the first derivative of Bessel function of the first kind.

Description

Calculates the zeros of the first derivatives of Bessel function.
Updates BessDerivZerosBisect.m with these changes:
1. Allows for m = 0
2. Allow the user to specify the particular m and k values desired.
3. Allows for a tolerance input parameter
4. Uses a table look-up to get closer initializations for small values of m and k.
5. Adds error checking
6. Computes the derivative w.r.t. to x rather than w.r.t. m (although the old method works, too.)

2011/05/11 Used Vincent's improvements.

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
BessDerivZerosBisect

• MATLAB release: MATLAB 7.10 (2010a)

[Vincent]

Thanks for this.

However, it tends to crash for high values of m and k > 1. (cf. for instance m=44 and k=4)

I think I fixed it, though, by replacing lines 103 to 110 by:

        while JprimeL*JprimeR > 0
            if(JprimeL > 0)
                Aleft = Aleft - (Aright - Aleft)/2;
                JprimeL=besselderiv(Aleft,m);
            else
                Aright = Aright + (Aright - Aleft)/2;
                JprimeR=besselderiv(Aright,m);
            end
        end

[Chandana]

Thank you, Carey smith and Vincent. You saved my time. Very useful work for my modeling.
Thank you again.