Quantized state systems method

The quantized state systems (QSS) methods [CK06] are a family of numerical integration solvers based on the idea of state quantization.

First-order QSS method – QSS1

Let an initial value problem be specified as follows.

{\dot {x}}=f(t,x),\quad x(t_{0})=x_{0}.

QSS1 approximates the above system by

{\dot {x}}=f(t,q)

where $x$ and $q$ are related by histeretic quantization functions.

The QSS Methods can be implemented as a discrete event system and simulated in any DEVS simulator.

QSS methods constitute the main numerical solver for PowerDEVS [BK011] software. They have also been implemented in as a stand alone version

[CK06] Francois E. Cellier and Ernesto Kofman (2006). Continuous System Simulation (first ed.). Springer. ISBN 978-0-387-26102-7.

[BK11] Bergero, Federico and Kofman, Ernesto (2011). "PowerDEVS: a tool for hybrid system modeling and real-time simulation" (first ed.). Society for Computer Simulation International,San Diego.{{cite news}}: CS1 maint: multiple names: authors list (link)

v t e Numerical methods for ordinary differential equations
First-order methods	Euler method Backward Euler Semi-implicit Euler Exponential Euler
Second-order methods	Verlet integration Velocity Verlet Trapezoidal rule Beeman's algorithm Midpoint method Heun's method Newmark-beta method Leapfrog integration
Higher-order methods	Exponential integrator Runge–Kutta methods List of Runge–Kutta methods Linear multistep method General linear methods Backward differentiation formula Yoshida Gauss–Legendre method
Theory	Symplectic integrator