On the potentiality of sequential and parallel codes based on extended trapezoidal rules (ETRs)

The Boundary Value Methods (BVMs) is a class of numerical methods for solving ODEs proposed and analyzed in the last few years. They are based on Linear Multistep Formulae (LMF) and do not suffer from the theoretical order limitations due to the Dahlquist barriers. In previous papers some families of BVMs have been proposed and studied. In this paper we exploit the possibility of using the family of Extended Trapezoidal Rules (ETRs) to construct both a sequential and a parallel code. Such methods are used in a block form which improves their flexibility, even though in this form some stability problems arise. The potentiality of the resulting codes are shown through comparison on some test problems taken from the literature. (C) 1997 Elsevier Science B.V.