Multi-time-scale dynamics of road–vehicle systems

This paper investigates higher order simulation schemes and associated covariance equations, extended correspondingly. The methods are derived by means of multiply iterated integrals and applied to road–vehicle systems. To avoid numerical instabilities in case of high vehicle speeds, multi-time-scale dynamics are introduced by scaling the time and noise increments according to the main system frequencies. In the stationary case, the covariances are time-invariant so that Euler schemes can be applied with bigger time steps without systematic errors. Note that deterministic methods as the classical Runge–Kutta approach are consistently applicable to the drift term only, but not to the diffusion of stochastic differential equations.