Variational Iteration Technique and Some Methods for the Approximate Solution of Nonlinear Equations

Abstract

In this paper, we suggest and analyze a new recurrence relation which generates the iterative methods of higher order for solving nonlinear equation f(x) = 0. This general recurrence relation is obtained by using variational iteration technique. We purpose some new iterative methods for solving nonlinear equations. We also test different examples to illustrate the efficienc y of these new methods. Comparison with other similar methods is also given. These new methods can also be considered as alternative to the existing methods. This technique can be applied to suggest a wide class of new iterative methods for solving nonlinear equations.