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β-blocked multistep methods for Euler-Lagrange DAEs: Linear analysis

Arévalo, Carmen LU ; Führer, Claus LU and Söderlind, Gustaf LU (1997) In ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik 77(8). p.609-617
Abstract
Many different methods have been suggested for the numerical solution of index 2 and 3 Euler-Lagrange equations. We focus on 0-stability of multistep methods (φ, σ) and investigate the relations between some well-known computational techniques. By various modifications, referred to as β-blocking of the σ polynomial, some basic shortcomings of multistep methods may be overcome. This approach is related to projection techniques and has a clear and well-known analogy in control theory. In particular, it is not necessary to use BDF methods for the solution of high index problems; indeed, “nonstiff” methods may be used for part of the system provided that the state-space form is nonstiff. We illustrate the techniques and demonstrate the results... (More)
Many different methods have been suggested for the numerical solution of index 2 and 3 Euler-Lagrange equations. We focus on 0-stability of multistep methods (φ, σ) and investigate the relations between some well-known computational techniques. By various modifications, referred to as β-blocking of the σ polynomial, some basic shortcomings of multistep methods may be overcome. This approach is related to projection techniques and has a clear and well-known analogy in control theory. In particular, it is not necessary to use BDF methods for the solution of high index problems; indeed, “nonstiff” methods may be used for part of the system provided that the state-space form is nonstiff. We illustrate the techniques and demonstrate the results with a simplified multibody model of a truck. (Less)
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organization
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type
Contribution to journal
publication status
published
subject
in
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
volume
77
issue
8
pages
9 pages
publisher
John Wiley & Sons
external identifiers
  • Scopus:4244129535
ISSN
0044-2267
DOI
10.1002/zamm.19970770813
language
English
LU publication?
yes
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47e7754f-9d37-4140-91f9-586d7268c213
date added to LUP
2017-02-08 09:29:17
date last changed
2017-02-27 11:32:02
@article{47e7754f-9d37-4140-91f9-586d7268c213,
  abstract     = {Many different methods have been suggested for the numerical solution of index 2 and 3 Euler-Lagrange equations. We focus on 0-stability of multistep methods (φ, σ) and investigate the relations between some well-known computational techniques. By various modifications, referred to as β-blocking of the σ polynomial, some basic shortcomings of multistep methods may be overcome. This approach is related to projection techniques and has a clear and well-known analogy in control theory. In particular, it is not necessary to use BDF methods for the solution of high index problems; indeed, “nonstiff” methods may be used for part of the system provided that the state-space form is nonstiff. We illustrate the techniques and demonstrate the results with a simplified multibody model of a truck.},
  author       = {Arévalo, Carmen and Führer, Claus and Söderlind, Gustaf},
  issn         = {0044-2267},
  language     = {eng},
  number       = {8},
  pages        = {609--617},
  publisher    = {John Wiley & Sons},
  series       = {ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik},
  title        = {β-blocked multistep methods for Euler-Lagrange DAEs: Linear analysis},
  url          = {http://dx.doi.org/10.1002/zamm.19970770813},
  volume       = {77},
  year         = {1997},
}