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In this paper, we suggest and analyze a new class of iterative methods for solving nonlinear equations by using the homotopy perturbation method. Convergence of their method is also considered. Here we also discuss the efficiency index and computational order of convergence of new methods. Several numerical examples are given to illustrate the efficiency(More)
In this paper, we suggest and analyze a new two-step iterative method without second derivatives for solving nonlinear equations. We prove that the modified method has a fourth-order convergence. The efficiency index of this new method is 4 1/3 = 1.58. Several examples are given to illustrate the efficiency and the performance of the new method. The new(More)
In this paper, we suggest and analyze some new higher-order iterative methods free from second derivative for solving nonlinear equations. Per iteration, these new methods require three evaluations of the function and two of its first-derivative with efficiency index = Convergence of their methods is also considered. Several numerical examples are given to(More)
In a recent paper, Noor and Noor [K. Inayat Noor, M. Aslam Noor, Predictor–corrector Halley method for nonlinear equations, Appl. Math. Comput., in press, doi:10.1016/j.amc.11.023] have suggested and analyzed a predictor–corrector method Halley method for solving nonlinear equations. In this paper, we modified this method by using the finite difference(More)
In this paper, we suggest and analyze some new higher-order iterative methods by using Householder's method free from second derivative for solving nonlinear equations. Here we use new and different technique for implementation of higher-order derivative of the function and derive new higher-order predictor-corrector iterative methods free from second(More)
In this paper, we used Hamiltonian for nonlinear oscillators with discontinuities. The maximal relative error for the frequency obtained by new variational method compared with the exact solution indicates the remarkable precision of this method. Some examples are given to illustrate the effectiveness and convenience of the method. 1. INTRODUCTION There are(More)
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