DETERMINATION OF OPTIMUM ACCELERATING FACTORS FOR SUCCESSIVE OVER-RELAXATION ON AN EQUIDISTANT AND NON-EQUIDISTANT RECTANGULAR NET

A modification to the successive overrelaxation iterative procedure for solving elliptic partial differential equations is presented. The modified method is based on an extension of Brazier's nodal overrelaxation method in one dimension, characterised by the use of a different overrelaxation factor for each point in the net. The extension to several dimensions make use of the separability of the variables for the error distribution. Thus the optimum one dimensional results are directly used in the several dimensional problem. The present method has been examined in one and two dimensions, for equidistant and non-equidistant nets. The computational time required to obtain a given accuracy for a solution was found for all two dimensional cases to be half (or less) of that required by conventional methods. © 1979.