Discrete QMR and BCG in the numerical solution of linear systems of ODEs

In this paper we consider the use of QMR and BCG in the numerical solution of linear systems of ODEs reformulated as second kind integral equations. The implementation of the methods is performed in practice by applying them on suitably discretized equations. An important issue in this contest is to compare the behaviour of the discrete and continuous iteration. Here we consider the case of linear systems of ODEs. The discretization is performed using a continuous Runge-Kutta method. A numerical experiment concludes the paper.