Table 1 CPU times consumed by the different ODE solvers, to integrate Eq. (9) for 10 000 dimensionless time units with the additional term, i.e., as for Fig. 1 (b, d, and f). Here \(\Delta \tau\) and \(\varepsilon\) were chosen, according to the intersections of the horizontal dotted lines in Fig. 2 (b, d, and f), to ensure that \(\max \left\{ \left| \left| \textbf{m}\right| -1 \right| \right\} \le 10^{-13}\) throughout the entire integration time. Other parameters are the same as in Fig. 1. The CPU time refers to an Intel Xeon CPU, model E5-2690 v4 @ 2.60GHz.
From: Stabilisation of the Landau-Lifshitz-Gilbert equation for numerical solution via standard methods
Method | CPU seconds | \(\varvec{\Delta \tau }\) or \(\varvec{\varepsilon }\) |
|---|---|---|
RK4 | 486 | \(1.5 \times 10^{-3 \, \, \, \, }\) |
RK4GILL | 625 | \(1.5 \times 10^{-3 \, \, \, \, }\) |
RK5 | 124 | \(1.0 \times 10^{-2 \, \, \, \, }\) |
DOPRI5 | 56 | \(2.1 \times 10^{-13}\) |
DOP853 | 15 | \(2.8 \times 10^{-13}\) |
RK5PS | 363 | \(3.2 \times 10^{-3 \, \, \, \, }\) |
GL2 | 2033 | \(2.2 \times 10^{-3 \, \, \, \, }\) |
