Towards a reliable implementation of least-squares collocation for higher-index differential-algebraic equations
Numerical Analysis
2020-11-26 v1 Numerical Analysis
Abstract
In this note we discuss several questions concerning the implementation of overdetermined least-squares collocation methods for higher-index differential algebraic equations (DAEs). Since higher-index DAEs lead to ill-posed problems in natural settings, the dicrete counterparts are expected to be very sensitive, what attaches particular importance to their implementation. We provide a robust selection of basis functions and collocation points to design the discrete problem and substantiate a procedure for its numerical solution. Additionally, a number of new error estimates are proven that support some of the design decisions.
Keywords
Cite
@article{arxiv.2011.12611,
title = {Towards a reliable implementation of least-squares collocation for higher-index differential-algebraic equations},
author = {Michael Hanke and Roswitha März},
journal= {arXiv preprint arXiv:2011.12611},
year = {2020}
}