A Deterministic-Stochastic Hybrid Integrator for Random Ordinary Differential Equations with Aerospace Applications

This is the authors' abstract. We don't add key points for this paper.

High-fidelity propagation of dynamical systems can become a cumbersome task when dealing with uncertainties modeled as random processes. The random ordinary differential equations usually describing the uncertain dynamics can be numerically integrated, but they are challenging from the computational point of view. Traditional methods usually require either the storage of a relevant amount of data or small integration steps. In this work, a hybrid method, embedding a stochastic integration method in a deterministic higher-order scheme, is conceived to obtain fast and stochastically correct results. The method is used for uncertainty propagation and quantification of aerospace problems. Results show a reduction of at least one order of magnitude for both computational time and memory usage with respect to state-of-the-art techniques, while it is able to provide statistically correct results.