A parallel preconditioning technique for boundary value methods *

Brugnano, L. and D. Trigiante, A parallel preconditioning technique for boundary value methods, Applied Numerical Mathematics 13 (1993) 277-290. The boundary value methods (BVMS) are a class of numerical methods for solving initial value problems for ODES [3,7,14]. One reason that prevented their diffusion in the past years was their higher cost, with respect to the standard initial value methods. We show that BVMs may become competitive when they are efficiently implemented on parallel or vector computers. Since they require the solution of large, sparse block linear systems, usually obtained by using an iterative method, a preconditioning 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 reported.