Abstract:
This article discusses a two-step iterative method to solve a nonlinear equation. The
method is obtained by substituting the quadratic formula into Taylor expansion,
then the second derivative that appears in the formula is estimated using a cubic
polynomial. Analytically it is showed, using the Taylor expansion, geometric series
and binomial series that the iterative method has the convergence of order six and
requires four function evaluations for each iteration. The proposed method is optimal
and based on its efficiency index 1.57. Numerical computations show that the new
method is comparable to the other discussed six-order methods.
