What do you mean by "work"?

It may be that the proof of global convergence of Newton's method requires a third derivative.  However, I'm sure that many circuit simulators converge fine even when some of the functions don't even have second derivatives.  They're not using strict Newton-Raphson (there's some damping of the steps), and they're not guaranteed to converge -- they just "usually" do.

oh really.

Now I have another very basic question. Why is Newton Raphson method "dominates" circuit simulation methods?

Hi Peter....thanks I hope I "will" come up with such a better method ....