Linearly Implicit Quantization-Based Integration Methods for Stiff Ordinary Differential Equations

MIGONI, GUSTAVO; MARIO BORTOLOTTO; ERNESTO KOFMAN; FRANÇOIS CELLIER

SIMULATION MODELLING PRACTICE AND THEORY

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2013 vol. 35 p. 118 - 136

1569-190X

In this paper, new integration methods for stiff ordinary differential equations (ODEs) are developed. Following the idea of quantization--based integration (QBI), i.e., replacing the time discretization by state quantization, the proposed algorithms generalize the idea of linearly implicit algorithms. Also, the implementation of the new algorithms in a DEVS simulation tool is discussed. The efficiency of these new methods is verified by comparing their performance in the simulation of two benchmark problems with that of other numerical stiff ODE solvers. In particular, the advantages of these new algorithms for the simulation of electronic circuits are  demonstrated.