Telescopic Projective Methods for Sti Di erential Equations

Projective methods were introduced in an earlier paper as having potential for the eÆcient integration of problems with a large gap between two clusters in their eigenvalue spectrum, one cluster containing eigenvalues corresponding to components that have already been damped in the numerical solution and one corresponding to components that are still active. In this paper we introduce iterated projective methods that allow for explicit integration of sti problems that have a large spread of eigenvalues with no gaps or with several gaps in their spectrum.