MATLAB: Set of transcendental equations

Question

Hello,

Below is a transcendental equation that I would like to solve:

z*besselj(1,z) – c*besselj(0,z) = 0

where c is a constant and z is the variable to be determined. I know that I need to solve this using fzero(fun,x0) and I would like to use the initial value x0=1. However, I am struggling with "fun", i.e., I'm not sure how to make the above equation into the right format to use in fzero. Ultimately, I would like to make a list of solutions of z for each value of c from 0 to 225 with a step size of 0.01.

Anything helps!

Thanks,

John

Answer 1

I suggest:

f = @(z,c)  z.*besselj(1,z) - c.*besselj(0,z);

then call fzero with a vector of c values:

c = ...
for k1 = 1:length(c)
    ci = c(k1);
    z = fzero(@(z) f(z,ci), 1);
end

There are going to be an infinity of zeros for every value of c, so obviously more than one solution.