Research on the application of the parameter freezing precise exponential integrator in vehicle-road coupling vibration

The vehicle-road coupling dynamics problem is a prominent issue in transportation, drawing significant attention in recent years. These dynamic equations are characterized by high-dimensionality, coupling, and time-varying dynamics, making the exact solutions challenging to obtain. As a result, numerical integration methods are typically employed. However, conventional methods often suffer from low computational efficiency. To address this, this paper explores the application of the parameter freezing precise exponential integrator to vehicle-road coupling models. The model accounts for road roughness irregularities, incorporating all terms unrelated to the linear part into the algorithm's inhomogeneous vector. The general construction process of the algorithm is detailed. The validity of numerical results is verified through approximate analytical solutions (AASs), and the advantages of this method over traditional numerical integration methods are demonstrated. Multiple parameter freezing precise exponential integrator schemes are constructed based on the Runge-Kutta framework, with the fourth-order four-stage scheme identified as the optimal one. The study indicates that this method can quickly and accurately capture the dynamic system's vibration response, offering a new, efficient approach for numerical studies of high-dimensional vehicle-road coupling systems.