On the sensitivity of implementations of a least-squares collocation method for linear higher-index differential-algebraic equations

TL;DR

This paper analyzes the sensitivity and error sources of a least-squares collocation method for solving higher-index differential-algebraic equations, providing condition number estimates and error analysis to improve implementation robustness.

Contribution

It offers an analytic estimation of condition numbers and error sources for the collocation method applied to higher-index differential-algebraic equations, advancing understanding of implementation sensitivity.

Findings

Condition numbers vary with implementation choices

Error sources are identified and quantified

Guidelines for robust implementation are suggested

Abstract

The present paper continues our investigation of an implementation of a least-squares collocation method for higher-index differential-algebraic equations. In earlier papers, we were able to substantiate the choice of basis functions and collocation points for a robust implementation as well as algorithms for the solution of the discrete system. The present paper is devoted to an analytic estimation of condition numbers for different components of an implementation. We present error estimations, which show the sources for the different errors.