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Convergence of multistep discretizations of DAEs

Arévalo, Carmen LU and Söderlind, Gustaf LU (1995) In BIT 35(2). p.143-168
Abstract
Standard ODE methods such as linear multistep methods encounter difficulties when applied to differential-algebraic equations (DAEs) of index greater than 1. In particular, previous results for index 2 DAEs have practically ruled out the use of all explicit methods and of implicit multistep methods other than backward difference formulas (BDFs) because of stability considerations. In this paper we embed known results for semi-explicit index 1 and 2 DAEs in a more comprehensive theory based on compound multistep and one-leg discretizations. This explains and characterizes the necessary requirements that a method must fulfill in order to be applicable to semi-explicit DAEs. Thus we conclude that the most useful discretizations are those that... (More)
Standard ODE methods such as linear multistep methods encounter difficulties when applied to differential-algebraic equations (DAEs) of index greater than 1. In particular, previous results for index 2 DAEs have practically ruled out the use of all explicit methods and of implicit multistep methods other than backward difference formulas (BDFs) because of stability considerations. In this paper we embed known results for semi-explicit index 1 and 2 DAEs in a more comprehensive theory based on compound multistep and one-leg discretizations. This explains and characterizes the necessary requirements that a method must fulfill in order to be applicable to semi-explicit DAEs. Thus we conclude that the most useful discretizations are those that avoid discretization of the constraint. A freer use of e.g. explicit methods for the non-stiff differential part of the DAE is then possible. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
compound multistep methods, differential algebraic equations (DAE), multistep methods, one-leg methods, partitioned methods
in
BIT
volume
35
issue
2
pages
26 pages
publisher
Springer
external identifiers
  • scopus:0342669979
ISSN
0006-3835
DOI
10.1007/BF01737160
language
English
LU publication?
yes
id
06be806b-51f7-4897-838e-3cfc14289c28
date added to LUP
2017-02-08 09:47:18
date last changed
2017-05-02 10:40:47
@article{06be806b-51f7-4897-838e-3cfc14289c28,
  abstract     = {Standard ODE methods such as linear multistep methods encounter difficulties when applied to differential-algebraic equations (DAEs) of index greater than 1. In particular, previous results for index 2 DAEs have practically ruled out the use of all explicit methods and of implicit multistep methods other than backward difference formulas (BDFs) because of stability considerations. In this paper we embed known results for semi-explicit index 1 and 2 DAEs in a more comprehensive theory based on compound multistep and one-leg discretizations. This explains and characterizes the necessary requirements that a method must fulfill in order to be applicable to semi-explicit DAEs. Thus we conclude that the most useful discretizations are those that avoid discretization of the constraint. A freer use of e.g. explicit methods for the non-stiff differential part of the DAE is then possible.},
  author       = {Arévalo, Carmen and Söderlind, Gustaf},
  issn         = {0006-3835},
  keyword      = {compound multistep methods,differential algebraic equations (DAE),multistep methods,one-leg methods,partitioned methods},
  language     = {eng},
  number       = {2},
  pages        = {143--168},
  publisher    = {Springer},
  series       = {BIT},
  title        = {Convergence of multistep discretizations of DAEs},
  url          = {http://dx.doi.org/ 10.1007/BF01737160},
  volume       = {35},
  year         = {1995},
}