Generalized Multistep Methods

Abstract

The search for higher order A -stable multistep methods is carried out in two main directions:

• Use higher derivatives of the solutions;

• Throw in additional stages, off-step points, super-future points and the like, which leads into the large field of general linear methods.

The Dahlquist bound of two on the order of A -stable multistep methods was the imperative to propound ... weaker stability properties, ... An alternative approach for circumventing Dahlquist’s bound is to modify the class of methods, rather than the property.

(T.A. Bickart & W.B. Rubin 1974)