Explicit De-couple Group AOR method for solving elliptic partial differential equations

The explicit group successive overrelaxation (EGSOR) methods which approximates the solution of the sparse linear systems derived from the discretisation of self-adjoint elliptic partial differential equations have been presented (Yousif & Evans, 1986) and it has been shown that these methods are faster and with a smaller computational effort in comparison with the implicit 1-line and 2-line block successive overrelaxation (SOR) iterative methods. Martins, Yousif and Evans (2002) introduced a new explicit 4-point group accelerated overrelaxation (EGAOR) iterative method and made a comparison with the point AOR method for the model problem showing its computational advantages. The aim of this paper is to present an explicit 4-point de-coupled group accelerated overrelaxation iterative (EDGAOR) method and to show that it is faster than the explicit 4-point group accelerated overrelaxation (EGAOR) iterative method.