On General Linearly Implicit Quantized State System Methods

TL;DR

This paper introduces new numerical integration algorithms for ODEs based on state quantization, enhancing existing LIQSS methods with improved performance while maintaining stability and error bounds.

Contribution

It generalizes LIQSS methods and develops two novel sub-families that outperform current algorithms in efficiency and stability.

Findings

New algorithms improve performance over classic methods

Preserve stability and error bounds

Demonstrated advantages in application examples

Abstract

This work proposes a methodology to develop new numerical integration algorithms for ordinary differential equations based on state quantization, generalizing the notions of Linearly Implicit Quantized State Systems (LIQSS) methods. Using this idea, two novel sub-families of algorithms are designed that improve the performance of current LIQSS methods while preserving their properties regarding stability, global error bound and efficient event handling capabilities. The features of the new algorithms are studied in two application examples where the advantages over classic numerical integration algorithms is also analyzed.