Some New Iterative Methods for Nonlinear Equations

Abstract

We suggest and analyze some new iterative methods for solving the nonlinear equationsf(x)=0using the decomposition technique coupled with the system of equations. We prove that new methods have convergence of fourth order. Several numerical examples are given to illustrate the efficiency and performance of the new methods. Comparison with other similar methods is given.

Solving Strongly Nonlinear Oscillators by New Numerical Method

“…DJM has been used to create a new predictor-corrector method [21,22]. Noor et al [23,24,25,26,27] used DJM to create numerical methods to handle algebraic equations. Here the Daftardar-Gejji and Jafari method will be discussed, which successfully used to solve differential equations and nonlinear equations in the form:…”

New iterative technique for solving a system of nonlinear equations

“…This idea has been used by Noor [36] to develop some iterative methods for solving nonlinear equations. Noor et al [41][42][43][44][45][46][47][48] have used the idea of coupled system of equations with the new decomposition technique to develop several iterative methods for solving nonlinear equations. In this paper, the technique and ideas of [48] are extended for solving the system of nonlinear equations.…”

Derivative-Free Iterative Methods for Solving Nonlinear Equations

“…Using (2), in well known Newton method, we obtain the following derivative-free iterative method for solving nonlinear equation as: Algorithm2.1. For a given x 0 , find the approximation solution x n+1 by the following iterative scheme: He [2], Noor [5] and Noor and Noor [7], suggested the iterative method for solving nonlinear equation which involves the first derivative of the function is described as: Algorithm2.2 [2,5]. For a given x 0 , find the approximation solution x n+1 by the following iterative scheme:…”

“…Algorithm2.4 [7]. For a given x 0 , find the approximation solution x n+1 by the following iterative scheme:…”