Abstract:
This article discusses the modification of Golbabai-Javidi method by approximating
the second derivative with a cubic polynomial to solve nonlinear equations. Analyt-
ically, using Taylor expansion and geometric series, the proposed method is proven
to have a sixth order of convergence and it has efficiency index 1.565. Numerical
computation of several examples with some other mentioned methods shows that
the proposed method in general has the smallest error in its approximation to the
root of the nonlinear equations. Next, the dynamic of proposed method is displayed
using basin of attraction.