Boundary Value Methods (BVMs) are a relatively new class of numerical methods for ODEs based on LMF (see [1]). In [2,3] a parallel version of such methods has been proposed, exploiting a parallelism across the steps. Subsequently, the problem of the mesh selection and the convergence of the parallel nonlinear iteration has been studied in [4,5]. Nevertheless, some problems were raised in [5], concerning the computational cost of the parallel solver. In this talk, it is shown how some of these problenms have been fixed, by introducing a suitable modification of block BVMs.

[1] L.Brugnano, D.Trigiante. Solving Differential Problems by Multistep Initial and Boundary Value Methods. Gordon and Breach, Amsterdam, 1998.

[2] P.Amodio, L.Brugnano. Parallel Implementation of Block Boundary Value Methods for ODEs. J. CAM 78 (1997) 197-211.

[3] P.Amodio, L.Brugnano. Parallel ODE Solver Based on Block BVMs. Adv. Comput. Math. 7,1-2 (1997) 5-26.

[4] L.Brugnano, D.Trigiante. Parallel Implementation of Block Boundary Value Methods on Nonlinear Problems: Theoretical Results. APNUM 28 (1998) 127-141.

[5] P.Amodio, L.Brugnano. ParalleloGAM: a Parallel Code for ODEs. APNUM 28 (1998) 95-106.

MINISIMPOSIUM SESSION: 19. Representation and implementation of variable step multistep methods