solve Bassel function matlab

I am trying to solve a Bessel function depending of a variable "x", for that reason I am using the fsolve command:

%%myfun

function F = myfun(x)
F = [1.5*(1-x)*besselj(0,x)-x*bessely(0,x)*(x.^2-1)];

%%main file

x0 = [0; 0];           
[x,fval] = fsolve(@myfun,x0)

I do not understand what I am doing wrong.

Regards

Answer 1

[John D'Errico]

myfun is a function of ONE variable, x. There is only ONE unknown, so x should be a scalar.

But if that is true, then why have you provided a VECTOR starting value in x0?

Answer 2

[Star Strider]

You need to (1.) vectorize every multiplication and division in your function, as well as the exponentiation, and (2.) start a a point close to (not at) 0 in order to avoid fsolve throwing a ‘Objective function is returning undefined values at initial point. FSOLVE cannot continue.’ error.

This works:

myfun = @(x) 1.5*(1-x).*besselj(0,x)-x.*bessely(0,x).*(x.^2-1);

x0 = [1; 1]*eps;           
[x,fval] = fsolve(myfun,x0);