On the Numerical Analysis of Elliptic Boundary Value Problems by the Successive Over relaxation Method (Report 1)

The successive over relaxation method is an effective iterative method for solving the difference analogue of an elliptic partial differential equation. But its main difficulty is that the optimum relaxation factor for any given problem can not usually be found prior to getting the solution. We^ have proposed an empirical new method, practical successive over relaxation method, for solving the Dirichlet problem. This computational method was named NIKI\u27s method by Radlley et al.^3. In this paper, we describe the proposed method and report the results of it and two other methods of successive over relaxation method by applying them to same problems