Explicit group USSOR method for solving elliptic partial differential equations

This paper presents a new 4-points Explicit Group Unsymmetric Successive Overrelaxation (USSOR) iterative method to approximate the solution of the linear systems derived from the discretisation of self-adjoint elliptic partial equations. Several studies have been carried out by many researchers on the USSOR iterative method, for example, the analysis of its convergence [1], an upper bound for its error [2] and recently a special case of the USSOR, namely the SSOR method has been used to approximate the solution of augmented systems [4] and [8]. The computational behaviour of this new method and a comparison with its point version is presented.