The explicit group TOR method

The numerical methods for solving partial differential equations have been one of the significant achievements made possible by the digital computers. With the advent of parallel computers, many studies have been performed and a number of new techniques have been investigated in order to develop new methods that are suitable for these computers. One of these techniques is the explicit group iterative methods which have been extensively studied and analysed in the last two decades. The explicit group iterative methods for the numerical solution of self-adjoint elliptic partial differential equations have been introduced (Evans & Biggins, 1982; Yousif & Evans, 1986) and has been shown to be computationally superior in comparison with other iterative methods. These methods were found to be suitable for parallel computers as they possess independent tasks (Evans & Yousif, 1990). Martins, Yousif & Evans (2002) introduced a new explicit 4-points group accelerated overrelaxation (EGAOR) iterative method, a comparison with the point AOR method has shown its computational advantages. The point TOR method was developed and a number of papers related to the TOR method and its convergence have been presented (Kuang & Ji, 1988; Chang, 1996; Chang, 2001; Martins, Trigo & Evans 2003). In this paper, we formulate a new group method from the TOR family, the explicit 4-points group overrrelaxation (EGTOR) iterative method, the derivation of the new method is presented. Numerical experiments have been carried out and the results obtained confirm the superiority of the new method when compared to the point TOR method.