Some variants of Newton's method with fifth-order and four-order convergence for solving nonlinear equations

Chun's two-step predictor-corrector type iterative method for solving nonlinear equations (Iterative Methods Improving Newton's Method by the Decomposition Method, J . Comput. Math. Appl.50, 1559-1568 ) is improved and a kind of new iterative method is presented. Some present methods derived from Adomian Decomposition method are unified in a form and a series of new methods with high convergence order and the value of EFF are obtained by introducing parameter also. Those methods can be considered as a significant improvement of the Newton's method and its variant forms.