Improving Linearly Implicit Quantized State System Methods

Abstract

In this article we propose a modification to Linearly Implicit Quantized State System Methods (LIQSS), a family of methods for solving stiff Ordinary Differential Equations (ODEs) that replace the classic time discretization by the quantization of the state variables. LIQSS methods were designed to efficiently simulate stiff systems, but they only work when the system has a particular structure. The proposed modification overcomes this limitation, allowing the algorithms to efficiently simulate stiff systems with more general structures. Besides describing the new methods and their algorithmic descriptions, the article analyzes the algorithms performance in the simulation of some complex systems.