Newton Raphson Application from paper I just want to double check that I'm understanding the method followed in this paper.
They provide a flow chart with the method followed here.
The equations used are provided here:
Specifically equation 12,18,19.
I'm doing the procedure using python's scipy.optimize.newton lib.
So for the first procedure I initialize Vt,Rs and Rsh to a guess that is some common value.


*

*Step 1:
Then they say to do Vt = f(Rs,Rsh) so what I did was take equation 12, move the Impp to the right to form -Impp + rest of equation = 0. I then use newton rhapson to return a value of Vt where the equation is equal to 0 for the guessed Rs and Rsh.

*Step 2:
I then move onto the next step Rsh = f(Rs, Vt) and here I take equation 19, take -1/Rsh over so that the equation is -1/Rsh + the rest of equation =  0. Then I sub in the prior calculated Vt from step 1 and the guess of Rs.

*Step 3: After this I check whether equation 18 is equal to zero subbing in the calculated Rsh and Vt from step 2 and 1 respectively.

*Step 4: If the obtained value doesn't fulfil Step 3, I select a random value between credible values for Rsh and repeat Steps 1-3.
I just want to double check whether I'm understanding this correctly, namely how there applying newton rhapson to these equations, because I haven't been able to obtain an answer close to something logical using this. Are I doing these three steps correctly as outlined by the flow diagram?
Thank you in advance for any help!
 A: That's very peculiar! At that website it says "Newton-Raphson or Bisection Method" but those are very different.  In either case you do NOT "select a random value between credible values".  Newton-Raphson and bisection can be used to solve equations of the form f(x)= 0, where "x" can represent a multivariable vector. 
To use "bisection" you have to initially find values, a and b, such that f(a)< 0 and f(b)> 0 (or f(a)> 0 and f(b)< 0).  As long as f is a continuous function, there must be a point between a and b where f(x)= 0.  We have no idea exactly where that point is but it is reasonable to try the midpoint, c= (a+ b)/2.  If f(c) is not 0 it must differ in sign from either f(a) or f(b) so we know there is a zero in one of those two intervals, a to c or c to b.  Every time we do that we reduce the size of the interval by 1/2.
To use "Newton-Raphson" we must first require that f be differentiable. Choose a to be any value of x.  If f(a) is not 0 (and if is we are done), we calculate f'(a).  Then y= f'(a)(x- a)+ f(a) is the line tangent to the curve y= f(x) at x= a.  Since the
tangent line is a good approximation to the curve (most often) we can approximate a root of the equation by a root of that linear function:  f'(a)(x- a)+ f(a)= 0.  That gives f'(a)(x- a)= -f(a) so x- a= -f(a)/f'(a) and then x= a- f(a)/f'(a).  If that value of x does not satisfy the equation, repeat with a= that value of x.
