A new free derivatives method based on the inverse interpolation for solving nonlinear equations

AbstractThe paper is concerned with a multipoints iterative method for approximating a simple zero z of a real valued function. This method is essentially based on the idea to extend secant method to be an inverse interpolation of degree greater than 1. We prove that for a sufficiently smooth function f in a neighborhood of z the order of convergence is at least 1 + √3. Using Mathematica with its higher precision computation, we present some numerical examples to illustrate the theoretical results and to compare our method with the others given in the literature.