A computational method for determining the optimum relaxation factor for successive over relaxation (SOR) method for the solution of large linear systems

The availability of very high speed automatic digital13; computers with lsrge and fast Bemories has made it possible13; to solve problems which although algorithms for handling13; them were well-known previously could not be used in practice because the number of calculations required would have been prohibitive. One such example is that of solving a13; large system of linear equations where the matrix of the13; system is very sparse that is most of its elements are13; zeros. Such system often arise in the numerical solution13; of elliptic partial differential equations by finite difference methods. In practice such problems arise in a variety of fields such as fluid flow, elasticity, steady state heat flow and weather prediction. Usually iterative methods are used to solve such problems an extensive mathematical theory has been developed in this direction