6.2.2 Pseudo-Transient Method

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].