New iterative technique for solving nonlinear equations

New iterative technique for solving a system of nonlinear equations

“…It is the generalization of the fourth-order convergent family of methods of Noor et al [48] for solving the system of nonlinear equations F(X) = 0.…”

“…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.…”

New Family of Iterative Methods for Solving Nonlinear Models

“…The said decomposition technique is quite simple as compared to the ADM as it does not need the higher order derivatives of functions. This technique has extensively been used to develop some useful algorithms for solving nonlinear equations [4,5,10,18]. In 2015, Noor et al [18], using the same decomposition technique along with the idea of coupled system, proposed two fourth-order iterative methods ( [18], Algorithms 2.12 and 2.13) with efficiency index of 1.2600 each.…”

“…This technique has extensively been used to develop some useful algorithms for solving nonlinear equations [4,5,10,18]. In 2015, Noor et al [18], using the same decomposition technique along with the idea of coupled system, proposed two fourth-order iterative methods ( [18], Algorithms 2.12 and 2.13) with efficiency index of 1.2600 each. In this work, using the quadrature formula along with the fundamental law of calculus, truncating the series of ( ) at quadratic level and decomposition technique of [5], we construct a family of new iterative methods for solving nonlinear equations.…”

“…The convergence criteria of newly constructed families are also presented. In order to demonstrate the validity and better efficiency of our proposed methods, we solve the nonlinear equations arising in the population model and in the motion of a particle on an inclined plane [18]. We also present the graphical analysis for the endorsement of numerical results.…”