Regular and singular β-blocking of difference corrected multistep methods for nonstiff index-2 DAEs
Arévalo, Carmen; Führer, Claus; Söderlind, Gustaf (2000). Regular and singular β-blocking of difference corrected multistep methods for nonstiff index-2 DAEs. Applied Numerical Mathematics, 35, (4), 293 - 305
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Published
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English
Authors:
Arévalo, Carmen
;
Führer, Claus
;
Söderlind, Gustaf
Department:
Mathematics (Faculty of Engineering)
Numerical Analysis
Research Group:
Numerical Analysis
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.
Keywords:
Differential algebraic equations (DAE) ;
β-blocked methods ;
Multistep methods ;
Partitioned methods ;
Half-explicit methods ;
Difference corrected multistep methods
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