Newton raphson tranfsorm from 1d to 2d

i have the solution for a 1d problem. How to solve it in 2d ?

1D:

function [x] = my_NR(fun, dfun, x_0,E_tol)
q = 1;
E = inf;
x(q) = x_0;
while E > E_tol
    x(q+1) = x(q) - (fun(x(q)))/(dfun(x(q)));
    E = abs(x(q+1)-x(q));
    q = q+1;
end
end

How to do it in 2D ?

e.g

Input : f = @(x)[0.5*cos(x(1))-0.5*sin(x(2))-x(1);0.5*sin(x(1))+0.5*cos(x(2)-x(2))];
J = @(x)[-0.5*sin(x(1))-1,-0.5*cos(x(2));0.5*cos(x(1)),-0.5*sin(x(2))-1];
x_0 =[0 0]';
E_tol = 10E-04;
Output: x = [0.0 0.0 ;0.2 0.6;0.2287 0.5423;0.2291 0.5391]

[David Wilson]

The Newton-Rhapson is generally specific to 1D. If you want the more general nD case, you need to use the (multivariable) Newton scheme. See e.g. http://fourier.eng.hmc.edu/e176/lectures/NM/node21.html

or of course look up Wikipedia

https://en.wikipedia.org/wiki/Newton%27s_method#Nonlinear_systems_of_equations

If you want to just solve your particular problem then try fsolve.

By the way, do you really mean (in the 2nd equation of f(x))

cos(x(2)-x(2))

And is J above the Jacobian? (It's not what I compute!)