Fifth-order iterative methods for solving 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.

A SIXTH ORDER METHOD FOR SOLVING NONLINEAR EQUATIONS

In this paper, we present a new iterative method with order of convergence eighth for solving nonlinear equations. Periteration this method requires three evaluations of the function and one evaluation of its first derivative. A general error analysis providing the eighth order of convergence is given. Several numerical examples are given to illustrate the efficiency and performance of the new ...

Seventh-order iterative algorithm free from second derivative for solving algebraic nonlinear equations

Solving systems of nonlinear equations using decomposition technique

A systematic way is presented for the construction of multi-step iterative method with frozen Jacobian. The inclusion of an auxiliary function is discussed. The presented analysis shows that how to incorporate auxiliary function in a way that we can keep the order of convergence and computational cost of Newton multi-step method. The auxiliary function provides us the way to overcome the singul...

A New Fifth Order Derivative Free Newton-Type Method for Solving Nonlinear Equations

The present paper deals with fifth order convergent Newton-type with and without derivative iterative methods for estimating a simple root of nonlinear equations. The error equations are used to establish the fifth order of convergence of the proposed iterative methods. Finally, various numerical comparisons are made using MATLAB to demonstrate the performence of the developed methods.

A new iterative with memory class for solving nonlinear ‎equations‎

In this work we develop a new optimal without memory class for approximating a simple root of a nonlinear equation. This class includes three parameters. Therefore, we try to derive some with memory methods so that the convergence order increases as high as possible. Some numerical examples are also ‎presented.‎‎