New classes of iterative methods for nonlinear equations

摘要

In this paper, we suggest and analyze some new iterative methods for solving nonlinear equations f(x)=0 by using the variational iteration technique. These new methods includes the Householder and its variant forms as special cases. We also give several examples to illustrate the efficiency of these methods. Comparison with other similar methods is also given. These new methods can be considered as an alternative to the Newton method. This technique can be used to suggest a wide class of new iterative methods for solving system of nonlinear equations.