Paper Info
Title
Towards a reliable implementation of least-squares collocation for higher index differential-algebraic equations-Part 1: basics and ansatz function choices
Abstract
In the two parts of the present 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 discrete counterparts are expected to be very sensitive, which attaches particular importance to their implementation. In the present Part 1, we provide a robust selection of basis functions and collocation points to design the discrete problem. We substantiate a procedure for its numerical solution later in Part 2. Additionally, in Part 1, a number of new error estimates are proven that support some of the design decisions.
Year
DOI
Venue
2022
10.1007/s11075-021-01140-7
NUMERICAL ALGORITHMS
Keywords
DocType
Volume
Least-squares collocation, Higher index differential-algebraic equations, Ill-posed problem
Journal
89
Issue
ISSN
Citations 
3
1017-1398
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Michael Hanke100.68
Roswitha März22510.56