Dave describes a technique for avoiding needing to invert the full admittance matrix with an initial example given for a resistor whose value might change in time, though the idea is developed further to apply to the linearised contribution of a diode (which I may have further questions on later). Essentially the (unknown) current is placed on the RHS (source vector) then determined from voltage differences of the solution (I think).

I have a couple of questions:

1. to solve for voltages, surely I need to put

*something*for I_R into my source vector in order to solve my linear system? But I can't work out I_R until I solve for node voltages (can I?) so I_R remains unknown until after the linear system solve? I can see how I could do this analytically (see below) but I can't always expect analytic expressions (e.g. for a very complex system)

2. are the a_n, a_m, b_n, b_m trivially found from the remaining MNA A matrix numerically/by inspection and if so how? I can't quite connect the dots here!

My attempt at using this method, for a voltage divider with R1/R2 (with R1 variable) is shown below. I've done this

*symbolically*, but am struggling to see how to do it for arbitrary (more complex) examples. Basically I'd like to know how to do this "programatically".