Regular and singular β-blocking of difference corrected multistep methods for nonstiff index-2 DAEs
Författare
Summary, in English
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.
Avdelning/ar
- Matematik LTH
- Numerical Analysis
Publiceringsår
2000
Språk
Engelska
Sidor
293-305
Publikation/Tidskrift/Serie
Applied Numerical Mathematics
Volym
35
Issue
4
Länkar
- Publication in Lund University research portal
- 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
- http://dx.doi.org/10.1016/S0168-9274(99)00142-7
Dokumenttyp
Artikel i tidskrift
Förlag
Elsevier
Ämne
- Mathematics
Nyckelord
- Differential algebraic equations (DAE)
- β-blocked methods
- Multistep methods
- Partitioned methods
- Half-explicit methods
- Difference corrected multistep methods
Status
Published
Forskningsgrupp
- Numerical Analysis
ISBN/ISSN/Övrigt
- ISSN: 0168-9274