Parallel implementation of block boundary value methods on nonlinear problems: theoretical results

Abstract

Recently a new parallel ODE solver implementing a “parallelism across the steps” has been proposed (Amodio and Brugnano, 1997; Brugnano and Trigiante, 1998). In the mentioned references, the attention was devoted to some essential features of the parallel method, which are already present in the case where it is used to approximate linear continuous problems. In this paper, the previous analysis is completed by discussing questions which typically arise when approximating nonlinear continuous problems. In particular, we shall study, for the parallel solver, the problem of the mesh selection and the convergence of the nonlinear iteration.