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• A semi-recursive vehicle model is validated in modeling and accuracy. • Constant and adaptive time-step algorithms for real-time simulation are presented. • An accurate real-time simulation of a vehicle is completed in an affordable laptop. • A benchmark problem for the multibody dynamics community is put forward. Semi-recursive formulations and their various versions have made it possible to describe complex nonlinear systems such as vehicles precisely while still solving the relevant equations of motion in real time. An optimal combination of an efficient multibody formulation and a fast numerical time integration scheme are needed to accurately simulate complex systems in real time. This paper introduces a double-step semi-recursive multibody formulation and analyzes its performance with high-order numerical time-integration algorithms for real-time simulation. The Runge-Kutta, Gill, Runge-Kutta-Fehlberg, Adams-Bashforth-Moulton, and adaptive time step Runge-Kutta numerical methods are explained and compared. Results are verified against a commercial multibody software solution. A 15-degree-of-freedom sedan vehicle model serves as a benchmark to verify the theoretical results. The results highlight the differences between the numerical algorithms and suggest appropriate approaches for a nonlinear vehicle dynamics model, particularly for cases where simulation times are long. [ABSTRACT FROM AUTHOR]