New Fourth and Fifth-Order Iterative Methods for Solving Nonlinear Equations

Fifth-order iterative methods for solving nonlinear equations

In this paper, we suggest and analyze a new two-step iterative method for solving nonlinear equation f(x) = 0 by rewriting the given nonlinear equation as a coupled system of equations and using the Taylor series. It is shown that this new iterative method is of fifth-order. Several examples are given to illustrate its performance and efficiency. Comparison with other methods is also given. Thi...

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 eighth-order iterative methods for solving nonlinear equations

In this paper, three new families of eighth-order iterative methods for solving simple roots of nonlinear equations are developed by using weight function methods. Per iteration these iterative methods require three evaluations of the function and one evaluation of the first derivative. This implies that the efficiency index of the developed methods is 1.682, which is optimal according to Kung ...

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

THIRD-ORDER AND FOURTH-ORDER ITERATIVE METHODS FREE FROM SECOND DERIVATIVE FOR FINDING MULTIPLE ROOTS OF NONLINEAR EQUATIONS

In this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. Each of them requires one evaluation of the function and two of its first derivative per iteration. Several numerical examples are given to illustrate the performance of the presented methods.