Some numerical methods for solving nonlinear equations by using decomposition technique

In this paper, we use the system of coupled equations involving an auxiliary function together with decomposition technique to suggest and analyze some new classes of iterative methods for solving nonlinear equations. These new methods include the Halley method and its variant forms as special cases. Various numerical examples are given to illustrate the efficiency and performance of the new methods. These new iterative methods may be viewed as an addition and generalization of the existing methods for solving nonlinear equations.