Parallel iteration schemes for implicit ODEIVP methods

In this contribution to the Proceedings of the “International Symposium on New Aspects of Numerical Analysis in the Light of Recent Technology” held at Stresa on 13 until 18 September 1993, we give a survey of recent research at CWI for solving the implicit relations arising in ODEIVP methods on parallel computers. Starting with a General Linear method as introduced by Butcher, three forms of parallelism for solving the associated implicit equations are discussed, viz. (i) parallelism across the stages within a single step (stage parallelism), (ii) parallel preconditioners, and (iii) parallelism across the steps (step parallelism). The structure of these type of parallel methods will be described.