Parallel implementation of block boundary value methods for ODEs

The parallel solution of initial value problems for ODEs has been the subject of much research in the last thirty years, and different approaches to the problem have been devised. In this paper we examine the parallel methods derived by block boundary value methods (BVMs), recently introduced for approximating Hamiltonian problems. Here we restrict the analysis of the methods when applied to linear problems, since their nonlinear parallel implementation deserves further study. However, for linear problems, the methods can reach a high parallel efficiency.Some of these solvers can also be adapted for approximating continuous two-point boundary value problems. Numerical tests carried out on a distributed memory parallel computer are reported.