In this paper, a combination of Laplace transform and variational iteration method are applied to get an approximate analytic solution for the multi-pantograph delay with higher order differential equations. Lagrange multiplier technique is constructed a correction functional which obtained by using Laplace transform with the variational theory. Numerical studies for the application of the present method for the considered problems are given and graphically illustrated, our proposed method is compared favorably with other methods. The simplicity and efficiency of the method.

In this paper, we have suggested and analyzed a new two-step type iterative methods for solving nonlinear equations of the type. We show that this new two-step method is cubic convergence method. It is proved that this method is better than the Newton method and all results in (Soheili et al., 2008). Several examples are given to illustrate the efficiency of this new method and its comparison with other methods. This method can se considered as a significant improvement of the Newton method and its variant forms.

In this paper, we propose and discuss a new higher-order iterative method for solving nonlinear equations. This method based on a Halley and Householder iterative method and using predictor-corrector technique. The convergence analysis of our method is discussed. It is established that the new method has convergence order eighteen. Numerical tests show that the new method is comparable with the well-known existing methods and gives better results.

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