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 bas ed on Linear Multistep Formulae (LMF) and do not suffer from the theor etical order limitations due to the Dahlquist barriers. In previous pa pers some families of BVMs have been proposed and studied. In this pap er we exploit the possibility of using the family of Extended Trapezoi dal Rules (ETRs) to construct both a sequential and a parallel code. S uch methods are used in a block form which improves their flexibility, even though in this form some stability problems arise. The potential ity of the resulting codes are shown through comparison on some test p roblems taken from the literature. (C) 1997 Elsevier Science B.V.