i want to find the solution to an equation containing bessel function x*besselj(​1,x)-C*bes​selj(0,x). I am using newton raphson method but I am getting NaN as the root.

clc
close all
x=linspace(0,100,10^6);
Bi=0.1;
error=10;
for i=1:10^6
    x(i+1)=x(i)-(x(i).*besselj(1,x(i))-Bi*besselj(0,x(i)))./(x(i).*besselj(0,x(i))+Bi*besselj(1,(x(i))));
    err(i)=abs((x(i+1)-x(i))/x(i));
    if err(i)<error;
        break
    end
end
    root=x(i)

This is my code, could anyone please point out the errors?

Answer 1

[Walter Roberson]

x(1) is 0. besselj(1,0) is 0 and Bi*0 is 0. besslj(0,0) is 1, but you multiply that by x(1) which is 0. So your denominator of your expression is 0. The numerator is non-zero and positive so you get infinity as the result of the division.

That infinity then poisons everything else.

[Venkitesh1300]

so should I take a very small value which like 1e-10 to make the initial guess non zero?

[Walter Roberson]

Why not use fsolve() with initial guess 1 ?