| Title | Regular and singular β-blocking of difference corrected multistep methods for nonstiff index-2 DAEs |
| Authors | Carmen Arévalo, Claus Führer, Gustaf Söderlind |
| Alternative Location | http://www.sciencedirect.co..., Restricted Access |
| Alternative Location | http://dx.doi.org/10.1016/S..., Restricted Access |
| Publication | Applied Numerical Mathematics |
| Year | 2000 |
| Volume | 35 |
| Issue | 4 |
| Pages | 293 - 305 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | North-Holland |
| Abstract 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. |
| Keywords | Differential algebraic equations (DAE), β-blocked methods, Multistep methods, Partitioned methods, Half-explicit methods, Difference corrected multistep methods, |
| ISBN/ISSN/Other | ISSN: 01689274 |
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