Formal modeling and analysis of hybrid systems in rewriting logic using higher-order numerical methods and discrete-event detection

Formal modeling and analysis of interacting hybrid systems in HI-Maude: What happened at the 2010 Sauna World Championships?

“…This is consistent with our results in[22], where we compared the precision and execution times on a smaller case study for which the precise solution was available 11. The analyses yield the same result (in seconds) using the numerical methods rk2 and rk4.…”

“…On the other hand, Euler is the computationally fastest, whereas RK4 is the slowest. The experiments in [7,22] indicate, for the one example, that RK2 is a good compromise between precision and efficiency. The "step size" (or "time increment") between each visited point in time is the parameter of these approximation methods; the smaller the step size, the more accurate the numerical approximation, and the longer the computation time.…”

“…The papers [7,22] show the execution times and the relative errors for the different numerical methods on an example that does have an analytical solution, i.e., when we can compute the solved form of the differential equations. RK4 is the most sophisticated approximation algorithm of these, and Euler is the least sophisticated one.…”

“…We are not aware of any work using popular frameworks such as Simulink or KeYmeara to model the human thermoregulatory system. Among our own previous work, our paper [7] introduces the formal effort/flow-based object-oriented modeling technique for continuously interacting hybrid systems; the papers [42,22] describe how the Euler and the Runge-Kutta numerical approximation methods have been adapted to the effort/flow setting and then formalized/implemented in Maude. The papers [4,5] introduce the HI-Maude tool, and, finally, the paper [18] provides a shorter exposition of the sauna case study.…”

“…This execution is based on adaptations of the Euler [7], the Runge-Kutta 2nd order (RK2), and the Runge-Kutta 4th order (RK4) numerical approximation methods [22] to the effort/flow framework. The papers [7,22] show the execution times and the relative errors for the different numerical methods on an example that does have an analytical solution, i.e., when we can compute the solved form of the differential equations.…”