Continuous Time Simulation in a Discrete Event Framework using a Quantized State System Approach

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Simulating complex dynamical systems is difficult when models are large, stiff, and discontinuous. Traditional numerical solvers are reliable, but they often face limitations in such settings. Quantized State System (QSS) methods offer an alternative integration paradigm: they update only variables whose values change, making them efficient in large stiff and discontinuous systems. In this thesis, I refine QSS techniques with new update formulations, improved cycle detection, and Jacobian‑based coefficient computation for better accuracy and speed. These advances are implemented in QuantizedSystemSolver.jl, an open‑source Julia package. Tests on continuous and hybrid models show that QSS methods perform robustly on large stiff systems and remain competitive across diverse discontinuous scenarios. The results highlight that solver efficiency depends on the combined effects of sparsity, stiffness, activity distribution, and event cost.