Fri Oct 24 23:07:13 EDT 2014

About circuit simulation

What method am I re-inventing?  The problem is a set of non-linear
differential equations with non-linear (equality) constraints.

Something like this[1]. Numerical Solution of Nonlinear Differential
Equations with Algebraic Constraints..

EDIT: The question to ask (or to find the right formulation for) is
what is so different about nonlinear ODEs when you couple them with
linear or nonlinear algebraic equations as compared to algebraic
equations or straight up ODEs where all unknowns have derivatives?

Maybe trying to re-invent isn't the best idea here.  But I'd love to
gain more insight by taking an autodiff approach to this problem.
Tools are readily available in rai.

Some faint bell... In [3] it is mentioned that equtions built up from
KCL can't be solved linearly if there are voltage sources.  Therefore
Norton equivalent current sources are used.  ( See next post ).

This hints at me naive in placing I and V on the same footing, hoping
for linear equations.  Is this so?  I didn't actually check that.  (
EDIT: There is no problem: equations are linear in I and V. )

The other interesting question: where does the asymmetry come from?
Any topological reason there why it's not neatly dual?

Following hunches here, but it looks like because spice is so
specific, the somewhat general approach I'm taking is not going to cut
it.  Maybe first it's best to implement a minimal spice?  Ok, wait [3]
is just for DC and AC analysis..  Transient analysis is different.

[1] http://epubs.siam.org/doi/abs/10.1137/0907049
[2] https://ccrma.stanford.edu/~dtyeh/papers/yeh07_dafx_distortion.pdf
[3] http://www3.imperial.ac.uk/pls/portallive/docs/1/7292571.PDF
[4] http://books.google.com/books/about/Inside_SPICE.html?id=oOVSAAAAMAAJ