Some High-Order Convergent Iterative Procedures for Nonlinear Systems with Local Convergence

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.

AN ITERATIVE METHOD WITH SIX-ORDER CONVERGENCE FOR SOLVING NONLINEAR EQUATIONS

Modification of Newtons method with higher-order convergence is presented. The modification of Newtons method is based on Frontinis three-order method. The new method requires two-step per iteration. Analysis of convergence demonstrates that the order of convergence is 6. Some numerical examples illustrate that the algorithm is more efficient and performs better than classical Newtons method and ...

An Iterative Method with Fifth-Order Convergence for Nonlinear Equations

In this paper, we suggest and analyze a new four-step iterative method for solving nonlinear equations involving only first derivative of the function using a new decomposition technique which is due to Noor [11] and Noor and Noor [16]. We show that this new iterative method has fifth-order of convergence. Several numerical examples are given to illustrate the efficiency and performance of the ...

High order quadrature based iterative method for approximating the solution of nonlinear equations

In this paper, weight function and composition technique is utilized to speeds up the convergence order and increase the efficiency of an existing quadrature based iterative method. This results in the proposition of its improved form from a two-point quadrature based method of convergence order ρ = 3 with efficiency index EI = 1:3161 to a three-point method of convergence order ρ = 8 with EI =...

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