Originally published in the Journal of Instrumentation: http://www.iop.org/EJ/journalIn this paper we study several fixed step and adaptive Runge-Kutta methods suitable for transporting track parameters through an inhomogeneous magnetic field. Moreover, we present a new adaptive Runge-Kutta-Nyström method which estimates the local error of the extrapolation without introducing extra stages to the original Runge-Kutta-Nyström method. Furthermore, these methods are compared for propagation accuracy and computing cost efficiency in the simultaneous track and error propagation (STEP) algorithm of the common ATLAS tracking software. The tests show the new adaptive Runge-Kutta-Nyström method to be the most computing cost efficient
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