PARALLEL IMPLEMENTATION OF BLOCK BOUNDARY-VALUE METHODS ON NONLINEAR PROBLEMS - THEORETICAL RESULTS

Recently a new parallel ODE solver implementing a ''parallelism across the steps'' has been proposed (Amodio and Brugnano, 1997; Brugnano an d Trigiante, 1998), In the mentioned references, the attention was dev oted to some essential features of the parallel method, which are alre ady present in the case where it is used to approximate linear continu ous problems. In this paper, the previous analysis is completed by dis cussing questions which typically arise when approximating nonlinear c ontinuous problems. In particular, we shall study, for the parallel so lver, the problem of the mesh selection and the convergence of the non linear iteration, (C) 1998 Elsevier Science B.V. and IMACS, All rights reserved.