MODIFIKASI METODE CHEBYSHEV ORDE TIGA UNTUK MENCARI AKAR GANDA TANPA MENGGUNAKAN TURUNAN (Modification of Chebyshev’s Method Cubic Convergence for Finding Multiple Roots without Employing Derivatives)

Abstract

The aim of this paper is performing modification of Chebyshev’s method for finding multiple roots of the nonlinear equation ( ) 0f x  by converting to  . This is an efficient method to obtain the multiple roots of the nonlinear equation with unknown multiplicity of the single root of new equation ( ) 0H x  roots m without employing any derivatives. The method is approximating solution based on the central-difference approximations to the first, second and third derivative. It is shown that the method has cubic convergence. Several examples illustrate that the convergence and efficiency of this modification are better than classical Newton and the other described methods. In order to show convergence properties of the proposed methods, several numerical examples are demonstrated.