PARALLEL METHODS FOR INITIAL-VALUE PROBLEMS

As scientific technology becomes increasingly more sophisticated, the production of more data and/or the modelling of more complex systems requires computers with ever-increasing computational power. In order to cope with this situation numerical algorithms have to be developed which allow the distribution of both data and code segments over large numbers of processors with the hope that problems that were insoluble in a sequential environment because of either (or both) accuracy and size constraints can now be solved in a parallel environment. This paper will present a review of recently developed techniques in the area of parallel numerical methods for initial value problems. It will focus mainly on two different approaches-parallelism across time and parallelism across space-but will also consider special techniques developed for certain classes of problems.