In this paper we extend the 4-point explicit de-coupled group (EDG) iterative method, Abdullah (1991), to the 6 and 9-poinl EDG methods for the solution of elliptic partial differential equations. We will show graphically the technique of implementing the new grouping. Performance results for the algorithms are presented and a comparison with the 4-point scheme confirm the new groups to be computationally superior. Further, the implementations of the parallel 4, 6 and 9-point EDG methods on the Sequent Balance 8000 multiprocessor arc discussed and results from experiments performed are presented.