An n--th Order Generalization of the Activity Measure for Continuous Systems

RODRIGO CASTRO; ERNESTO KOFMAN

Zurich

Workshop; Activity-Based Modeling & Simulation 2014; 2014

ETH Zurich

Abstract. In this work we present an analytical expression that generalizes the definition of activity measure in continuous time signals. We define the activity of order n and show that it allows to estimate the number of sections of polinomials up to order n that are needed to represent that signal with certain accuracy. We apply this concept to obtain a lower bound for the number of steps performed by  quantization?based integration algorithms in the simulation of ordinary differential equations. We performed a practical analysis over a first order example system, computing the activity of order n and comparing it with the number of steps required integration methods of different orders. Wecorroborated the theoretical predictions, which indicate that the activity measure can be used as a reference for assessing the suitability of  different algorithms depending on how close they perform in comparison with the theoretical lower bound. Finally, a discussion is provided which indicates that further research is needed in order to test the resultspresented in this work in the context of stiff systems.