A Priori Methods for the Determination of the Optimum Relaxation Factor for the Successive Overrelaxation Method

摘要

The paper is concerned with methods for estimating the optimum relaxation factor for use with the successive overrelaxation method for solving the linear system Au = b. Special attention is given to linear systems arising from the solution by finite difference methods of boundary value problems corresponding to separable elliptic partial differential equations. Two classes of methods are considered: one leads to exact results and is based on the solution of an eigenvalue problem associated with an ordinary difference equation; the other leads to approximate results and is based on the solution of an eigenvalue problem involving an ordinary differential equation. An example involving the equation (u sub xx) + (k/y)(u sub y) + (u sub yy) = 0 is treated in detail. (Author)