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 [email protected]?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.

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