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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
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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
project
Numerical Analysis and Scientific Computing
language
English
LU publication?
yes
additional info
The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)
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1aef6af6-4587-41bc-af0f-3143aae0b144 (old id 1414635)
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date added to LUP
2016-04-01 16:21:40
date last changed
2026-02-11 13:25:32
@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}},
  keywords     = {{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}},
  doi          = {{10.1016/S0168-9274(99)00142-7}},
  volume       = {{35}},
  year         = {{2000}},
}