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Software such as the PLECS interface to Simulink uses piecewise-linear approximation of the equations governing the elements of a circuit.
The circuit is treated as a completely linear network of ideal diodes.
Every time a diode switches from on to off or vice versa, the configuration of the linear network changes.
Adding more detail to the approximation of equations increases the accuracy of the simulation, but also increases its running time.

1.852 seconds.