A practical guide to piecewise pseudospectral collocation for Floquet multipliers of delay equations in MATLAB

TL;DR

This paper presents a MATLAB implementation of a piecewise pseudospectral collocation method for computing Floquet multipliers of delay equations, improving stability analysis of periodic solutions.

Contribution

It introduces a practical, piecewise approach to pseudospectral collocation for delay equations, with detailed MATLAB implementation and usage examples.

Findings

Enhanced numerical stability in Floquet multiplier computation

Effective handling of delay equations with piecewise methods

Practical MATLAB tools for stability analysis

Abstract

In recent years we provided numerical methods based on pseudospectral collocation for computing the Floquet multipliers of different types of delay equations, with the goal of studying the stability of their periodic solutions. The latest work of the series concerns the extension of these methods to a piecewise approach, in order to take the properties of numerically computed solutions into account. In this chapter we describe the MATLAB implementation of this method and provide practical usage examples.