Regular and singular β-blocking of difference corrected multistep methods for nonstiff index-2 DAEs

There are several approaches to using nonstiff implicit linear multistep methods for solving certain classes of semi-explicit index 2 DAEs. Using beta -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 beta -blocking. We interpret earlier results as regular beta -blocking and then develop singular B-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 rho 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 tau is selected by a minimax criterion for the moduli of the zeros of sigma + tau. The class of explicit methods suitable as beta -blocked methods is investigated. With singular beta -blocking, Adams-Moulton methods up to order 7 can be stabilized with the stabilized method corresponding to the Adams-Bashforth methods. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.