Adaptive-Step-Size Numerical Methods in Rewriting-Logic-Based Formal Analysis of Interacting Hybrid Systems

This paper focuses on the formal modeling, simulation, and analysis of interacting hybrid systems that influence each other’s continuous behaviors. We define in the rewriting-logic-based Real-Time Maude tool a method for the numerical approximation of the continuous dynamics specified by ordinary differential equations. We adapt the Runge-Kutta-Fehlberg 4/5 method to define an adaptive-step-size technique that allows a more accurate approximation with less computational effort than fixed-step-size techniques. We also present experimental results for two thermal systems using different error tolerances.