A New Derivative-Free Method to Solve Nonlinear Equations

Abstract

A new high-order derivative-free method for the solution of a nonlinear equation is developed. The novelty is the use of Traub’s method as a first step. The order is proven and demonstrated. It is also shown that the method has much fewer divergent points and runs faster than an optimal eighth-order derivative-free method.

Keywords

• derivative-free methods
• simple roots
• nonlinear equations