Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

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)
Please use this url to cite or link to this publication:
author
; and
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
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)
id
1aef6af6-4587-41bc-af0f-3143aae0b144 (old id 1414635)
alternative location
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
2016-04-01 16:21:40
date last changed
2022-01-28 19:06:54
@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}},
}