How to find besselh zeros?

Hello everyone! I am trying to find a zero of an equation using besselh function. The code I am using is:

        f=@(x) (besselh(-1,2,x)*0.5*a-besselh(1,2,x))-besselh(1,1,x)*b;
        chi=fsolve(f,x0,opts);

Where a,b,x0 are given, and might be complex. I wish to use this part of code inside of loop so I am not sure if writing a different function to myfun every time is useful. Using fsolve I got an error:

"Error using trustnleqn (line 28) Objective function is returning undefined values at initial point. FSOLVE cannot continue."

Error in fsolve (line 368) [x,FVAL,JACOB,EXITFLAG,OUTPUT,msgData]=...

Using fzero I got: "Error using fzero (line 242) Function values at interval endpoints must be finite and real."

Thank you very much in advance!

Omer

Answer 1

[Torsten]

Split in real and imaginary part and solve both imag(f(z))=0 and real(f(z))=0 simultaneously for z=x+1I*y using fsolve.

Best wishes

Torsten.

[Omer Hamburger]

Hi Torsten, Thank you for your quick response! Can you please write an example how to write it? fsolve and fzero can not solve it because it gives the error:

Undefined function 'real' for input arguments of type 'function_handle'.

Error in @(x)real(f)

When I try to define the different parts of the function as you suggested.

Thank you,

Omer

[Torsten]

f=@(x) [real((besselh(-1,2,x(1)+1I*x(2))*0.5*a-besselh(1,2,x(1)+1I*x(2)))-besselh(1,1,x(1)+1I*x(2))*b); 
        imag((besselh(-1,2,x(1)+1I*x(2))*0.5*a-besselh(1,2,x(1)+1I*x(2)))-besselh(1,1,x(1)+1I*x(2))*b)];
x0=[1 1];
chi=fsolve(f,x0,opts);

Best wishes

Torsten.

[Omer Hamburger]

Torsten, Thank you ver much! It worked like magic! Thank you! I need just a little bit of question regarding your code:

When I run this code from the command window it works and give me the answer, but when I try to run this section from the script calling a function that calculates this "chi" I get the next error:

Error using trustnleqn (line 28) Objective function is returning undefined values at initial point. FSOLVE cannot continue.

Error in fsolve (line 368) [x,FVAL,JACOB,EXITFLAG,OUTPUT,msgData]=...

Error in findzero (line 10) chi=fsolve(f,x0,opts);

What is wrong with fsolve this time?

Thank you very much, you have been very helpful so far and I am grateful for your help!

Best wishes,

Omer

[Torsten]

You defined a and b before in the script ?

If yes, please show the complete code you are using.

Best wishes

Torsten.

[Omer Hamburger]

The function is below:

function [ chi ] = findzero( val,a,b,a0)

opts = optimset('Diagnostics','off','Display','off'); if (val==1) f=@(x) [real(besselh(0,2,x(1)+1i*x(2)).*a+besselh(0,1,x(1)+1i*x(2)).*b);imag(besselh(0,2,x(1)+1i*x(2)).*a+besselh(0,1,x(1)+1i*x(2)).*b)];

        x0=[a0 a0];
        chi=fsolve(f,x0,opts);
        chi=chi(1)+1i*chi(2);
    else

        f=@(x) [real((besselh(-1,2,x(1)+1i*x(2))*0.5*a-besselh(1,2,x(1)+1i*x(2)))-besselh(1,1,x(1)+1i*x(2))*b); 
        imag((besselh(-1,2,x(1)+1i*x(2))*0.5*a-besselh(1,2,x(1)+1i*x(2)))-besselh(1,1,x(1)+1i*x(2))*b)];
        x0=[a0 a0];
        chi=fsolve(f,x0,opts);
        chi=chi(1)+1i*chi(2);

    end

end

(The code is also attached) I use this function inside a loop, and in each iteration I call this function with different a,b,a,a0 and val. If needed I can attach all the functions and scripts I use to run the whole code.

Thank you,

Omer

[Torsten]

Print a, b and a0 before the call to fsolve.

Check whether they are given values.

Best wishes

Torsten.

[Omer Hamburger]

Thank you Torsten,

This have been very helpful, I fixed the problem!

Thank you very much,

Omer