Int. J. Emerg. Sci., 3(2), 119-130, June 2013 ISSN: 2222-4254 © IJES 119 A Comparison of Iterative Methods for the Solution of Non-Linear Systems of equations Noreen Jamil Department of Computer Science, The University of Auckland, New Zealand njam031@aucklanduni.ac.nz Abstract. This paper presents different techniques to solve a set of nonlinear equations with the assumption that a solution exists. It involves Gauss-Seidel Method for solving non-linear systems of equations. It determines that how many more computations are required so that convergence may be achieved. The Gauss Seidel Method is computationally simpler than other non-linear solvers. Several methods for solution of nonlinear equations have been discussed and compared. Keywords: Iterative Methods, Non-linear equations. 1 INTRODUCTION Consider the system of non-linear equations f 1 (x 1 , x 1 , …, x n ) = 0 f 2 (x 1 , x 1 , …, x n ) = 0 f n (x 1 , x 1 , …, x n ) = 0 We can write it in compact form as F(X) = 0 Where the functions f 1 , f 2 , .. f n = 0 are the coordinate functions of F. Non-linear systems of equations appear in many disciplines such as engineering, mathematics, robotics and computer sciences because majority of physical systems are nonlinear in nature. There are possibilities that more than one solution exists of the polynomial equations contained in the mentioned system. Non-linear systems of equations are not easy to solve. Some of the equations can be linear, but not all of them. In some situations a system of equations can have multiple solutions. Many linear and non-linear problems are sparse, i.e. most linear coefficients in the corresponding matrix are zero so that the number of non-zero coefficients is O(n) with n being the number of variables [7]. Iterative methods do not spend processing time on coefficients that are zero. Direct methods, in contrast, usually lead to fill-in, i.e. coefficients change from an initial zero to a non-zero value during the execution of the algorithm. Such methods we therefore may weaken the sparsity and may have to deal with more coefficients, that makes the processing time slower. Therefore, iterative, indirect methods are