Parallel ODE solvers based on block BVMs

In this paper we deal with Boundary Value Methods (BVMs), which are methods recently introduced for the numerical approximation of initial value problems for ODEs. Such methods, based on linear multistep formulae (LMF), overcome the stability limitations due to the well-known Dahlquist barriers, and have been the subject of much research in the last years. This has led to the definition of a new stability framework, which generalizes the one stated by Dahlquist for LMF. Moreover, several aspects have been investigated, including the efficient stepsize control [17,25,26] and the application of the methods for approximating different kinds of problems such as BVPs, PDEs and DAEs [7,23,41]. Furthermore, a block version of such methods, recently proposed for approximating Hamiltonian problems [24], is able to provide an efficient parallel solver for ODE systems [3].