Quantized State System Simulation

The paper introduces a new family of numerical ODE solvers called Quantized State System (QSS) methods. Given a set of ODEs in its state-space representation, the QSS methods replace the classic time slicing by a quantization of the states, leading to an asynchronous discrete-event simulation model instead of a discretetime difference equation model. QSS methods applied to stable linear time-invariant systems give always practically stable numerical results, irrespective of the quantization adopted. Taking into account that the QSS methods are explicit algorithms, this property has strong theoretical implications and offers a promising perspective for applications such as real-time simulation of stiff systems, where implicit solutions are usually unacceptable. Also discussed are the main properties of the methods in the context of simulating discontinuous systems (the asynchronous nature of these algorithms gives them important advantages for discontinuity handling). Another class of systems that can be simulated by means of these algorithms are marginally stable (Hamiltonian) systems.