Regular and singular β-blocking of difference corrected multistep methods for nonstiff index-2 DAEs
(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:
https://lup.lub.lu.se/record/1414635
- author
- Arévalo, Carmen LU ; Führer, Claus LU and Söderlind, Gustaf LU
- organization
- publishing date
- 2000
- 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
- 2024-01-11 06:33:52
@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<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.}}, 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}}, }