New iterative technique for solving a system of nonlinear equations

Abstract

Various problems of pure and applied sciences can be studied in the unified frame work of the system of nonlinear equations. In this paper, a new family of iterative methods for solving a system of nonlinear equations is developed by using a new decomposition technique. The convergence of the new methods is proved. Efficiency index of the proposed methods is discussed and compared with some other well-known methods. The upper bounds of the error and the radius of convergence of the methods are also found. For the implementation and performance of the new methods, the combustion problem, streering problem and Van der Pol equation are solved and the results are compared with some existing methods. Several new iterative methods are derived from the general iterative scheme. Using the ideas and techniques of this paper, one may be able to suggest and investigate a wide class of iterative methods for solving the system of nonlinear equations. This is another direction of future research.