Comparing Synchronous and Asynchronous Variable Step Size Explicit ODE Solvers: A Simulation Study

The efficient integration of ordinary differential equations (ODEs) is an important topic in continuous and hybrid systems research. Current solutions involve variable step size solvers based on synchronous and asynchronous approaches. In this paper we evaluate, by means of simulation, the performance and accuracy of adaptive explicit asynchronous ODE solvers and we compare them with explicit synchronous solvers. Simulation results show that explicit synchronous solvers can exhibit better performance than the corresponding asynchronous methods. We consider a family of systems that can be dynamically partitioned into asynchronous clusters of synchronous ODEs. We show that the ability to independently solve each cluster can lead to significant computation gains.