Abstract
The Breiter-Nesborny-Vokrouhlicky geometric algorithm for nonautonomous Poisson systems is extended to higher orders. The effectiveness of this extension is exemplified by numerically solving the exactly solvable model of a classical single spin in a rotating magnetic field. Because this model exhibits very complicated periodic motion, after long time elapsed, the usual fourth-order Runge-Kutta algorithm yields a decaying trajectory that has departed significantly from the exact trajectory. We found that the fourth-order Breiter-Nesborny-Vokrouhlicky geometric algorithm of type B remained close to the exact trajectory even when we chose large time-steps for which the Runge-Kutta fourth-order algorithm miserably fails even at relatively short times.
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Oh, S.K. Higher-order extension of the Breiter-Nesborny-Vokrouhlicky geometric algorithm for nonautonomous Poisson systems and its application to the exactly solvable model of a classical spin in a rotating magnetic field. Journal of the Korean Physical Society 60, 613–620 (2012). https://doi.org/10.3938/jkps.60.613
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DOI: https://doi.org/10.3938/jkps.60.613