Continuetijdsimulatie in een raamwerk voor discrete gebeurtenissen met behulp van de gekwantiseerde-toestandsysteemaanpak

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Original abstract

The simulation of a continuous time model is often reduced to the numerical integration of ordinary Differential Equations. These equations can be a challenge if they contain stiffness and discontinuities. Classic methods perform multiple matrix inversions and iterations to deal with these issues which is costly when the system is large. Recently, a new family of numerical explicit and implicit solvers, called Quantized State System (QSS) and Linearly Implicit QSS (LiQSS) respectively, can efficiently handle discontinuities and stiffness. However, the LIQSS algorithms exhibit some limitations as they are based on the assumption of the presence of entries on the main diagonal of the Jacobian of the system, and this introduces oscillations in the solution of some systems. Currently, there are few attempts to solve this issue such as forcing the derivatives to zero at some conditions, and performing a simultaneous update at other conditions. Furthermore, mixed mode methods seem promising, but they require the detection of when and where the system might become stiff and what parts of the system present discontinuities. Therefore, The goal of this PhD is to investigate stiffness detection in the realm of QSS methods, find a better oscillation detection technique, and develop an efficient differential equation solver in the language "Julia" to be integrated in a discrete event simulation.

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