The performance of a Tau preconditioner on systems of ODEs

In this work, we investigate the new preconditioner of the Tau method, introduced by Ghoreishi and Mohammad Hosseini [13], on systems of ODEs. With a different and relatively straightforward view on the Tau formulation of systems of ODEs this preconditioner is reformulated and explained. An error analysis of the method is also addressed. Some numerical comparisons with the standard Chebyshev-Tau method and the preconditioned method of Cabos confirm the overall efficiency of this preconditioner for systems of ODEs as well.