Newton Raphson (code from slides)

function NewtonRaphsonMethod
i = 1;
p0 = initial value;            %initial conditions
N = 100;                            %maximum number of iterations
error = 0.0001;                %precision required
syms 'x'
f(x) = Colebrook function %function we are solving
df = diff(f);                       %differential of f(x)

while i <= N
    p = p0 - (f(p0)/df(p0));               %Newton-Raphson method
    if (abs(p - p0)/abs(p)) < error   %stopping criterion when difference between iterations is below tolerance
        fprintf('Solution is %f \n', double(p))
        return
    end
    i = i + 1;
    p0 = p;  %update p0
end

fprintf('Solution did not coverge within %d iterations at a required precision of %d \n', N, error)     %error for non-convergence within N iterations
end