Fig. 2
From: Stabilisation of the Landau-Lifshitz-Gilbert equation for numerical solution via standard methods
The maximum error, over the same integration period shown in Fig. 1, for different values of the fixed time step, \(\Delta \tau\), and error tolerance setting, \(\varepsilon\). Other parameters are the same as in Fig. 1. As before, \(\varepsilon\) is the absolute and relative error tolerance settings for the adaptive time step methods (DOPRI5 and DOP853), shown in (c) and (d). For comparison, the horizontal dotted lines in (b, d, e, and f) shows the typical error ( \(\max \left\{ \left| \left| \textbf{m}\right| -1 \right| \right\} \le 10^{-13 \,}\)) obtainable by the two methods (RK5PS and GL2) that do conserve \(\left| \textbf{m}\right|\), without the additional term in (9). The legend in each figure also shows a fitted formula for the CPU time consumed by each calculation, as a function of either \(\Delta \tau\) or \(\varepsilon\).
