Geoffrey_Coram
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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.
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