4.1.3 Comparison between the Shape Functions

As already mentioned above, the $\textsf {arctan}$ function provides a more accurate fit for the physical properties, but is numerically more expensive. In order to compare the shapes of the two different functions, they are plotted in such a way that they appear as similar as possible, as Fig. 4.1 shows. The coercive field is kept constant and the shape parameter $w$ is manipulated in order to minimize the average deviation.

Figure 4.1: Comparison of the $\textsf {arctan}$ and the $\textsf {tanh}$ shape function