The class of Backward Differentiation Formulae (BDF) is a very important tool for solving stiff ordinary differential equations. It has been used in many of the most important codes (DIFSUB, LSODE, LSODI). The reasons which justify such preference are essentially the following: 1) the function is evaluated at only one point, 2) the absolute stability region is large enough, at least for the lowest order methods. The most serious drawback of these methods concerns the order limitation for stable schemes. In this presentation, we give the theoretical results which confirm that a generalization of the BDF, called GBDF (Generalized BDF, see [1]) overcomes this limitation. In fact, for all order there exist exactly one GBDF which is A-stable.

[1] L.Brugnano, D.Trigiante. Solving Differential Problems by Multistep Initial and Boundary Value Methods. Gordon and Breach, Amsterdam, 1998.

MINISIMPOSIUM SESSION: 6. Novel methods for ODEs