set of transcendental equations

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

[Star Strider]

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.

[John Moseley]

Hi,

Thanks for your help. I have tried this:

f = @(z,c)  z.*besselj(1,z) - c.*besselj(0,z);
c = 0:0.01:225;
for k1 = 1:length(c)
    ci = c(k1);
    z = fzero(@(z) f(z,ci), 1);
end

and I get only one solution for z, which is the solution closest to x0=1 for c=225. However, I would like a list of solutions for z (near x0=1) for all of the c values defined by the vector I used above. (I understand I'll only get the first solution to the equation closest to x0=1 for each value of c). I am new to the "for" statements. Could you please point me in the right direction?

Thanks,

John

[Star Strider]

My error, sorry. I posted an earlier version without the subscript for z.

Change:

z = fzero(@(z) f(z,ci), 1);

to:

z(k1) = fzero(@(z) f(z,ci), 1);

and you should have all of them.

[John Moseley]

Ah, I see. This works perfectly. Thanks again.

John

[Star Strider]

My pleasure!

(The sincerest form of appreciation on MATLAB Answers is to accept the one that solves your problem. This helps others who may be looking for a solution to the same problem.)

[John Moseley]

I just remembered to do that. Sorry about that.

John

[Star Strider]

Thanks!

I also should have made sure I’d added the subscript to z in my first post.