An Improved R-order Convergence Derivative-Free Method for Solving Nonlinear Equations

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 ...

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

New Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations

A new family of eighth-order derivative-freemethods for solving nonlinear equations is presented. It is proved that these methods have the convergence order of eight. These new methods are derivative-free and only use four evaluations of the function per iteration. In fact, we have obtained the optimal order of convergence which supports the Kung and Traub conjecture. Kung and Traub conjectured...

A new optimal method of fourth-order convergence for solving nonlinear equations

In this paper, we present a fourth order method for computing simple roots of nonlinear equations by using suitable Taylor and weight function approximation. The method is based on Weerakoon-Fernando method [S. Weerakoon, G.I. Fernando, A variant of Newton's method with third-order convergence, Appl. Math. Lett. 17 (2000) 87-93]. The method is optimal, as it needs three evaluations per iterate,...

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...