Mixed-mode state–time discretization in ODE numerical integration

Abstract

This article introduces the joint usage of Quantized State System (QSS) methods and classic numerical integration algorithms in the simulation of continuous time systems described by systems of Ordinary Differential Equations (ODEs). The proposed mixed-mode scheme consists of splitting an ODE, using QSS algorithms where they perform better than classic algorithms (i.e., in presence of frequent discontinuities or stiffness under certain particular sparse structures) and using classic algorithms where they are a better choice. Besides describing the methodology – where the key issue is the interface between both algorithms – the article studies some properties of the resulting scheme including convergence and numerical stability. In addition, the performance of the proposed mixed-mode algorithm is analyzed in the simulation of two large systems with heterogeneous dynamics, showing an important reduction of the simulation times – more than one order of magnitude – compared to the most efficient QSS and classic approaches.