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Regular and singular β-blocking of difference corrected multistep methods for nonstiff index-2 DAEs

Arévalo, Carmen LU ; Führer, Claus LU and Söderlind, Gustaf LU (2000) In Applied Numerical Mathematics 35(4). p.293-305
Abstract
There are several approaches to using nonstiff implicit linear multistep methods for solving certain classes of semi-explicit index 2 DAEs. Using β-blocked discretizations (Arevalo et al., 1996) Adams-Moulton methods up to order 4 and difference corrected BDF (Soderlind, 1989) methods up to order 7 can be stabilized. As no extra matrix computations are required, this approach is an alternative to projection methods.Here we examine some variants of β-blocking. We interpret earlier results as regular β-blocking and then develop singular β-blocking. In this nongeneric case the stabilized formula is explicit, although the discretization of the DAE as a whole is implicit. We investigate which methods can be stabilized in a broad class of... (More)
There are several approaches to using nonstiff implicit linear multistep methods for solving certain classes of semi-explicit index 2 DAEs. Using β-blocked discretizations (Arevalo et al., 1996) Adams-Moulton methods up to order 4 and difference corrected BDF (Soderlind, 1989) methods up to order 7 can be stabilized. As no extra matrix computations are required, this approach is an alternative to projection methods.Here we examine some variants of β-blocking. We interpret earlier results as regular β-blocking and then develop singular β-blocking. In this nongeneric case the stabilized formula is explicit, although the discretization of the DAE as a whole is implicit. We investigate which methods can be stabilized in a broad class of implicit methods based on the BDF ρ polynomials. The class contains the BDF, Adams-Moulton and difference corrected BDF methods as well as other high order methods with small error constants. The stabilizing difference operator<space>τ is selected by a minimax criterion for the moduli of the zeros of σ+τ. The class of explicit methods suitable as β-blocked methods is investigated. With singular β-blocking, Adams-Moulton methods up to order 7 can be stabilized with the stabilized method corresponding to the Adams-Bashforth methods. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Differential algebraic equations (DAE), β-blocked methods, Multistep methods, Partitioned methods, Half-explicit methods, Difference corrected multistep methods
in
Applied Numerical Mathematics
volume
35
issue
4
pages
293 - 305
publisher
Elsevier
external identifiers
  • scopus:0343867265
ISSN
0168-9274
DOI
10.1016/S0168-9274(99)00142-7
language
English
LU publication?
yes
id
1aef6af6-4587-41bc-af0f-3143aae0b144 (old id 1414635)
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http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6TYD-41MJ22S-2-5&_cdi=5616&_user=745831&_orig=search&_coverDate=12%2F31%2F2000&_sk=999649995&view=c&wchp=dGLzVlz-zSkWA&_valck=1&md5=29ac3215771f9307f206e81b52f6dd33&ie=/sdarticle.pdf
date added to LUP
2009-06-12 12:53:19
date last changed
2017-02-13 13:10:02
@article{1aef6af6-4587-41bc-af0f-3143aae0b144,
  abstract     = {There are several approaches to using nonstiff implicit linear multistep methods for solving certain classes of semi-explicit index 2 DAEs. Using β-blocked discretizations (Arevalo et al., 1996) Adams-Moulton methods up to order 4 and difference corrected BDF (Soderlind, 1989) methods up to order 7 can be stabilized. As no extra matrix computations are required, this approach is an alternative to projection methods.Here we examine some variants of β-blocking. We interpret earlier results as regular β-blocking and then develop singular β-blocking. In this nongeneric case the stabilized formula is explicit, although the discretization of the DAE as a whole is implicit. We investigate which methods can be stabilized in a broad class of implicit methods based on the BDF ρ polynomials. The class contains the BDF, Adams-Moulton and difference corrected BDF methods as well as other high order methods with small error constants. The stabilizing difference operator&lt;space&gt;τ is selected by a minimax criterion for the moduli of the zeros of σ+τ. The class of explicit methods suitable as β-blocked methods is investigated. With singular β-blocking, Adams-Moulton methods up to order 7 can be stabilized with the stabilized method corresponding to the Adams-Bashforth methods.},
  author       = {Arévalo, Carmen and Führer, Claus and Söderlind, Gustaf},
  issn         = {0168-9274},
  keyword      = {Differential algebraic equations (DAE),β-blocked methods,Multistep methods,Partitioned methods,Half-explicit methods,Difference corrected multistep methods},
  language     = {eng},
  number       = {4},
  pages        = {293--305},
  publisher    = {Elsevier},
  series       = {Applied Numerical Mathematics},
  title        = {Regular and singular β-blocking of difference corrected multistep methods for nonstiff index-2 DAEs},
  url          = {http://dx.doi.org/10.1016/S0168-9274(99)00142-7},
  volume       = {35},
  year         = {2000},
}