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In this paper, we use the variational iteration technique to suggest some new iterative methods for solving nonlinear equations f (x) = 0. We also discuss the convergence criteria of these new iterative methods. Comparison with other similar methods is also given. These new methods can be considered as an alternative to the Newton method. We also give several examples to illustrate the efficiency of these methods. This technique can be used to suggest a wide class of new iterative methods for solving system of nonlinear equations.

Abstract:In this paper, we suggest and analyze a new family of iterative methods for finding zeros of multiplicity of nonlinear equations by using the variational iteration technique. These new methods include the Halley method and its variants forms as special cases. We also give several examples to illustrate the efficiency of these methods. Comparison with modified Newton method is also given. These new methods can be considered as an alternative to the modified Newton method. This technique can be used to suggest a wide class of new iterative methods for solving system of nonlinear equations.

In this paper, a unique decomposition technique is implemented along with an auxiliary function for the best implementation. Some new and efficient techniques are introduced and analyzed for nonlinear equations. These techniques are higher ordered in approaching to the root of nonlinear equations. Some existing classical methods such as the Newton method, Halley method, and Traub's approach and their various modified forms are the special cases of these newly purposed schemes. These new iterative schemes are a good addition in existing methods and are also a comprehensive and generalized form for finding the solution of nonlinear equations.INDEX TERMS Decomposition technique, iterative scheme, convergence analysis, newton method, numerical examples, coupled system of equations.

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