Step length control is a key element aﬀecting the computational eﬃciency of a
continuation method. It aﬀects the continuation method with two issues: (1) speed – how
fast the corrector converges to a speciﬁed accuracy, and (2) robustness – whether the
corrector converges to a true solution given a predicted point.

| (5.12) |

This scaling factor for step is limited to a maximum of 2 and is calculated from an error estimation between the predicted and corrected solutions as follows,

| (5.13) |

where is a damping factor, is a speciﬁed tolerance, and is given by

| (5.14) |