How can I numerically solve equations containing Bessel functions in MATLAB?

Question

I have confronted an equation containing Bessel functions of the first type on one side and modified Bessel functions of the second type on the other. I want to know its exact solutions (values of u). The equation is as follows:

u*besselj(s-1,u)/besselj(s,u)=-w*besselK(s-1,w)/besselk(s,w)

where s is an arbitrary integer number, for example 2.

w can be written as a function of u:

w=sqrt(1-u^2);

and so this equation has only one variable: u

I'm new to MATLAB. I have no idea about how I should approach this. Could anyone please help me?

Answer 1

A quick thing to try may be the FZERO function, a generic nonlinear zero finder. To learn how to use it, you can implement the examples given in the documentation. Then, rewrite your function so it can be input to fzero and see what you get..

(Note: I haven't tried this, but I just noticed there were no replies yet so maybe it's better than nothing.)