Recent advances in the parallel solution in time of ODEs

Abstract. The parallel solution of initial value problems for ordinary differential equations (ODE-IVPs) has been a very active field of investigation in the past years. In general, the possibility of using parallel computing in this setting concerns different aspects of the numerical solution of ODEs, usually depending on the parallel platform to be used and/or on the complexity of the problem to be solved. In this paper we review possible extensions of a parallel method proposed in the mid-nineties by the authors. Moreover, we analyze its connections with subsequent approaches to the parallel solution of ODE-IVPs, in particular the “Parareal ” algorithm