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The method applied by e.g., *ASTAP* [73,33] is called the
pseudo-transient method and can be considered a variant of the source stepping
algorithm. Instead of the original circuit a transient simulation on a
``pseudo'' circuit is performed.
A pseudo-inductor is inserted in series with each independent voltage source
and each non-linear voltage-defined branch, and a pseudo-capacitor is inserted
in parallel with each independent current source and each non-linear
current-defined branch. The initial conditions for these pseudo-reactances
are chosen such that the initial transient solution is zero.
A transient analysis is performed upon this pseudo-circuit. As the transition
from the zero solution to the final solution is of no interest in this
analysis, the truncation error can be ignored as long as the solution
converges to the correct equilibrium solution. For this reason, the timestep
chosen is not determined by accuracy considerations; instead, the timestep is
taken as large as possible, consistent only with the convergence of the Newton
algorithm [43].

*Tibor Grasser *

1999-05-31