How to solve ODEs in real-time HLA distributed simulation

In the context of the Research Platform for Embedded Systems Engineering (PRISE) Project, we are developing and maintaining a complete aircraft flight simulation using the High Level Architecture (HLA), an IEEE standard for distributed simulation. This complex distributed simulation is composed of different distributed HLA simulators (e.g., Flight Dynamics, Sensors), whose dynamic behaviors are implemented as Ordinary Differential Equations (ODEs). The resolution of these equations is done, locally for each simulator, by numerical integration with methods like Euler or Adams-Bashforth. The global behavior of this distributed simulation, where each component runs its own local resolution, is a key challenge. The main problem is to ensure the global simulation consistency and, in particular, the specific data flows between components with the correct temporal real-time behavior. This paper specifically addresses the problem of solving ODEs over an HLA distributed architecture and offers a complete study (specifications, implementation and validation) where several theoretical concepts and methods are discussed