Two-Step Boundary Value Methods in the Solution of ODES

In this paper, we study boundary value methods (BVM methods) for solving initial value problems. These methods give some advantages with respect to usual initial value methods for ODES: for instance, BVM methods may be implemented efficiently on parallel computers. We propose two classes of BVM methods based on linear two-step schemes and we study their BVstability regions. The convergence will be approached by considering the simple csse of a single linear differential equation. Numerical tests will be given both to illustrate the numerical features of these methods and to show the performance of the parallel implementation of some BVM methods with respect to usual codes for ODES.