A PARALLEL PRECONDITIONING TECHNIQUE FOR BOUNDARY-VALUE METHODS

The boundary value methods (BVMs) are a class of numerical methods for solving initial value problems for ODEs [3,7,14]. One reason that pre vented their diffusion in the past years was their higher cost, with r espect to the standard initial value methods. We show that BVMs may be come competitive when they are efficiently implemented on parallel or vector computers. Since they require the solution of large, sparse blo ck linear systems, usually obtained by using an iterative method, a pr econditioning technique is needed for their efficient implementation. In this paper we introduce and study a new preconditioning technique. Some numerical tests on a distributed memory parallel computer are rep orted.