I was learning to implement MNA(SPICE) and I am quite stuck near diodes . I read through a couple of sources and they instruct using Newton-Raphson to basically find the intersection of the load line and the diode IV curve iteratively .MNA for the circuit below proceeds as follows
$$\begin{bmatrix}1/R&-1/R&0&1\\-1/R&2/R+G&-G&0\\0&-G&G+1/R&0\\1&0&0&0\end{bmatrix}\begin{bmatrix}V1\\V2\\V3\\I1\end{bmatrix}=\begin{bmatrix}0\\-Ieq\\Ieq\\Vs\end{bmatrix}$$
Where \$Ieq\$ and \$G\$ are the current source and conductance of the diode companion model respectively .I'm lost at how to proceed further . I can't seem to understand where Newton-Raphson fits in here?