Fig. 1
From: Stabilisation of the Landau-Lifshitz-Gilbert equation for numerical solution via standard methods
Comparison of the absolute value of the error in \(\left| \textbf{m}\right|\) for the seven different time integration techniques used to solve (9), without (a,c and e) and with (b, d, and f) the additional term. In (a), (b), (e), and (f), the fixed time step was \(\Delta \tau = 0.01\), while for the two adaptive time step methods, shown in (c) and (d), the absolute and relative error tolerances were both equal to \(\varepsilon = 1\times 10^{-12}\). Other parameters: \(B = 0.5\), \(\omega = 0.5\), \(\alpha = 0.05\), and \(\Delta \tau = 0.01\). For additional details, see the main text surrounding this figure.
