Abstract:
This article discusses a two-step iterative method for solving nonlinear equations.
This method is obtained by modifying Newton’s method using a weight function.
Analytically, it is shown that using Taylor expansion and geometric series, this iter-
ation method has a convergence order of five and requires four function evaluations
for each iteration. This fifth order iteration method has an efficiency index of 1.495.
Numerical computations show the new method is comparable to other fifth-order
methods discussed. This article also discusses basins of attraction, namely a visual
depiction of the dynamic behavior of an iteration method for nonlinear equations
from various starting points.
