Step size selection in numerical differences using a regression kink

We propose a new step-size selection procedure for numerical differences based on fitting a piecewise linear shape to the observed estimate of truncation error and determining the position of its kink. The novelty of this method is in its use of the full information about the estimated total error behaviour at both sides around the optimum and in the incorporation of robust statistical tools for estimating the best V-shaped fit. The added safety checks ensure that the kink is detected if it exists, or a reasonable step size is returned in the case there is no kink. In numerical simulations, the proposed method algorithm outperforms two existing algorithms in terms of median error when tested on 5 well-behaved and 3 pathological functions.