This paper shows how to implement a semi-implicit algorithm based on the Adams-Bashforth algorithm as a predictor, and a second order Adams-Moulton procedure as a corrector in the Landau–Lifshitz–Gilbert-Slonczewski equation. We compare the results with a Runge-Kutta scheme of the 5th order, while for the standard problem #4 (and, in general, for the LLG equation) the computational speeds are of the same order, and we found better performance when the thermal fluctuations or the spin-polarized currents are taken into account.
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Giordano et al. (2012) studied this question.
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