In order to find an algorithm applicable for train running time simulation in timetabling and real-time control applications (conflict detection and resolution, driver advisory system), three state-of-the-art algorithms for running time computation are compared concerning calculation imprecisions and computation times which are the main requirements in those computations. Therefore the exact solution of the differential equation of movement of the infinitesimal calculus is compared with those of the numeric approximations by EULER'S method and GAUSS quadrature. A case study on German real-world tracks using three modern train configurations is performed. Additionally, the influences of mass modelling as mass strap or mass point and the possibility to emulate the mass strap behaviour by using a pre-computed slope profile is examined. Furthermore the influence of the detailedness of slope profiles on computation times and accuracy is analysed and a method which can be used for reducing the grade of detailedness of pre-computed slope profiles is shown. It is illustrated that high precision computations can only be carried out, when it is acceptable to use more computation time. In this context, the results reveal that this conflict of objectives can be solved by using a correctly parameterised EULER'S method, which can be used for all applications under examination as it offers a good trade-off between calculation time and preciseness. (C) 2014 Elsevier Ltd. All rights reserved.