A family of iterative methods with sixth and seventh order convergence for nonlinear equations

New iterative methods with seventh-order convergence for solving nonlinear equations

In this paper, seventh-order iterative methods for the solution ofnonlinear equations are presented. The new iterative methods are developed byusing weight function method and using an approximation for the last derivative,which reduces the required number of functional evaluations per step. Severalexamples are given to illustrate the eciency and the performance of the newiterative methods.

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

Three-Step Iterative Methods with Sixth-Order Convergence for Solving Nonlinear Equations

In this paper, we develop new families of sixth-order methods for solving simple zeros of non-linear equations. These methods are constructed such that the convergence is of order six. Each member of the families requires two evaluations of the given function and two of its derivative per iteration. These methods have more advantages than Newton’s method and other methods with the same converge...

A family of optimal iterative methods with fifth and tenth order convergence for solving nonlinear equations

In this paper, we propose a two-step method with fifth-order convergence and a family of optimal three-step method with tenth-order convergence for finding the simple roots of nonlinear equations. The optimal efficiency indices are all found to be 5 1 3 ≈ 1.71 and 10 1 4 ≈ 1.78. Some numerical examples illustrate that the algorithms are more efficient and performs better than other methods.

A Family of Optimal Derivative Free Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations

In this paper, modification of Steffensen’s method with eight-order convergence is presented. We propose a family of optimal three-step methods with eight-order convergence for solving the simple roots of nonlinear equations by using the weight function and interpolation methods. Per iteration this method requires four evaluations of the function which implies that the efficiency index of the d...