New Optimal Fourth-Order Iterative Method Based on Linear Combination Technique

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

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,...

new family of two-parameters iterative methods for non-linear equations with fourth-order convergence

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new family of two-parameters iterative methods for non-linear equations with fourth-order convergence

Optimal Fourth-order Iterative Methods Free from Derivatives

The construction of optimal fourth-order iterative schemes for solving univariate nonlinear equations is discussed. Per iteration, the methods consist of three evaluations of the function and they are free from any derivative calculation which property is so fruitful in engineering problems. We analytically show the fourth-order convergence. Numerical examples are considered to confirm the appl...