Chaotic Behavior of Stiff ODEs and Their Derivatives: An Illustrative Example

TL;DR

This paper presents an example demonstrating how numerical noise can induce chaos in the solutions of stiff ODEs during differentiation, highlighting challenges in numerical analysis of such systems.

Contribution

It provides an illustrative example showing chaos emergence in stiff ODEs due to computational noise, emphasizing difficulties in their differentiation.

Findings

Numerical noise can induce chaos in stiff ODE solutions.

Differentiating stiff ODEs can be problematic due to chaotic behavior.

The example highlights challenges in numerical methods for stiff systems.

Abstract

In the following, an illustrative example concerning difficulties in differentiating stiff ODEs is presented. In the given example, the solution of a completely deterministic system becomes chaotic due to computational noise introduced by the numerical algorithm.