A Novel Quantisation-based Integration Method for ODEs

Integration of Ordinary Differential Equations (ODE's) plays a paramount role in the dynamic simulation of a wide spectrum of processes in Chemical Engineering. This paper presents a novel approach within our discipline, namely the Quantised State Integration technique (QSI) (also known as Quantised State Simulation, QSS) which was introduced in its raw form several decades ago within Electrical Engineering for the simulation of electrical and electronic circuits in dynamic operation. While traditionally integration of ODE's considers time to be the coordinating parameter and it is discretised to allow the calculation of the state variables evolution, in QSS methods the states are discretised and time is calculated at points states go state events (changes by an amount equal to the discretisation level for each of them)-this allows effectively the decoupling of the state integration within accuracy tolerances. In the current work, we present significant theoretical and implementational extensions to the method, rendering it capable of handling large- to huge-scale applications involving stiff systems, state discontinuities (discrete events in hybrid systems) as well as the efficient calculation of sensitivity equations-all aspects that have previously been impossible to incorporate in the QSS suite of techniques presented over the years. Overall, all theoretical and preliminary computational demonstrations show it to be a very promising and powerful integration technique with a strong potential for future evolution and contributions. A multitude of areas that can benefit from this technique are identified in the pape