On some boundary value methods for stiff IVPs in ODEs

Abstract

A boundary value method (BVM) leads to a discrete boundary value problem with some conditions imposed at the initial points and the remaining ones at the final points. The interest in this class of methods is the fact that BVMs overcome the limitations of the well-known Dahlquist order and stability barrier for an A-stable linear multistep method (LMM). Yet, A-stability is fundamental to the integration of stiff ordinary differential equations (ODEs). This presents multiple families of linear multistep formulas (LMFs) with future points based on extended backward differentiation formula (BDF) which can be used as a main method in a BVM implementation for the solution of initial value problems (IVPs) in ODEs.