An Interval Step Control for Continuation Methods
Ralph Baker Kearfott, Zhaoyun Xing · SIAM Journal on Numerical Analysis · 1994
The authors present a step control for continuation methods that is deterministic in the sense that (i) it computationally but rigorously verifies that the corrector iteration will converge to a point on the same curve as the previous point (i.e., the predictor/corrector iteration will never jump across paths), and (ii) each predictor step is as large as possible, subject to verification that the curve is unique with the given interval extension. The authors present performance data and comparisons with an approximate step control method (PITCON version 6.1). A comparison of plots obtained from both step controls reveals that an approximate step control will behave erratically in situations where the interval step control leads to orderly progression along the curve. This is true even if the maximum allowable stepsize for the approximate method is set to be smaller than many of the steps actually taken by the interval algorithm. Limitations of interval step controls are also discussed.