Abstract:
This article discusses the modification of King’s method by using approximation
of first derivative with interpolation to solve nonlinear equations. Analytically, by
using Taylor expansion and geometric series, the proposed method is proven to
have an fourth order of convergence. The proposed method is derivative free and
based on Conjecture of Kung and Traub the new method attains optimality with
efficiency index 1.587. Numerical computations of several examples with some other
mentioned methods show that the proposed method in general has the smallest error
in its aprroximation root of the nonlinear equations.
