syms initial_R
u = -100;
alpha = 2;
v = initial_R*exp((2*(1-alpha))/(2+(1-alpha)*u*initial_R)/(2-alpha*u*initial_R)^(alpha)^2*(2+(1-alpha)*u*initial_R)^(1-alpha^2))
vpr = diff(v,initial_R);
y = matlabFunction(v)
ypr = matlabFunction(vpr)
kmax = 50;
initial_R_old = 1.0;
tol = 0.000001;
k = 0;
dx = 1.0;
while dx > tol && k < kmax
k = k+1;
initial_R_new = initial_R_old - y(initial_R_old)/ypr(initial_R_old);
dx = abs(initial_R_old - initial_R_new);
initial_R_old = initial_R_new;
end
initial_R_new
y(initial_R_new)

