Abstract
Several finite difference approximations which used only adjacent grid points for three-dimensional Poisson equation are proposed. In this paper, the optimal acceleration parameter and the optimal convergence rate of the SOR method for solving a linear system of equatins arising from those approximations with a rectangular region are investigated. We prove the red-black ordering SOR method to suited to vector processors is superior to the usual SOR method for one of those approximations, and study theoretically the optimal acceleration parameter and the optimal convergence rate of the red-black ordering SOR method for the approximation.
