Convergence of multistep discretizations of DAEs
(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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https://lup.lub.lu.se/record/06be806b-51f7-4897-838e-3cfc14289c28
- author
- Arévalo, Carmen LU and Söderlind, Gustaf LU
- organization
- publishing date
- 1995
- 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
- 2021-01-03 08:04:42
@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}}, keywords = {{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}}, doi = {{10.1007/BF01737160}}, volume = {{35}}, year = {{1995}}, }