A new mesh selection strategy for ODEs

In this paper a new mesh selection strategy, based on the conditioning properties of continuous problems, is presented. It turns out to be particularly efficient when approximating solutions of BVPs. The numerical methods used to test the reliability of the strategy are symmetric Linear Multistep Formulae (LMF) used as Boundary Value Methods (BVMs) since they provide a wide choice of methods of arbitrary high order and have similar stability properties to each other. In particular, we shall consider a subclass of such methods, called Top Order Methods (TOMs) (Amodio, 1996; Brugnano and Trigiante, 1995, 1996), to carry out the numerical results on some singular perturbation test problems.