Applied Numerical Mathematics 35 (2000) 293–305 Regular and singular β -blocking of difference corrected multistep methods for nonstiff index-2 DAEs Carmen Arévalo a,1 , Claus Führer b,2 , Gustaf Söderlind b,∗,2 a Department of Scientific Computing and Statistics, Simón Bolívar University, Apartado 89000, Caracas 1080-A, Venezuela b Numerical Analysis, Centre for Mathematical Sciences, Lund University, Box 118, S-221 00 Lund, Sweden Received 19 March 1999; received in revised form 19 November 1999 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 (Arévalo et al., 1996) Adams–Moulton methods up to order 4 and difference corrected BDF (Söderlind, 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 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.  2000 IMACS. Published by Elsevier Science B.V. All rights reserved Keywords: Differential algebraic equations (DAE); β -blocked methods; Multistep methods; Partitioned methods; Half-explicit methods; Difference corrected multistep methods 1. Introduction We shall consider linear multistep discretizations of the general semi-explicit index 2 DAE in Hessenberg form * Corresponding author. E-mail addresses: camena@cesma.usb.ve (C. Arévalo), Claus.Fuhrer@na.lu.se (C. Führer), Gustaf.Soderlind@na.lu.se (G. Söderlind). 1 Partially funded by Simón Bolívar University Project DID-S1-CB-118 and CONICIT contract G-97-000592. 2 Partially funded by TFR contracts 222/96-520 and 222/95-546. 0168-9274/00/$ – see front matter  2000 IMACS. Published by Elsevier Science B.V. All rights reserved PII:S0168-9274(99)00142-7