Modifikasi metode iterasi berorde tiga dengan orde konvergensi optimal

Abstract

Weerakoon-Fernando’s and Homeier’s methods are a third-order iterative method to solve nonlinear equations. A new third-order iterative method is constructed  by sum of Weerakoon-Fernandon’s and Homeier’s method. This paper discusses  the modification of the third-order iterative method using contra harmonic mean with  involving one real parameter q. The aim of this modification is  to improve the convergence order of the method and keep the number of function evaluations. Based on the result of study shows that the method has a third-order of convergence for  and a fourth-order of convergence for  with three evaluation of functions. Furthermore, numerical simulation is given to exam  the perfomance of the methods. The measurement  of performance of the methods, such as : number of iterations, number of function evaluations, numerical convergence  order, and value of function, are compared with Newton’s, Weerakoon-Fernando’s, and Homeier’s methods. Generally, the result of  numerical simulation shows that the new method for  has better  performance than others.

Keywords: Weerakoon-Fernando’s method, Homeier’smethod, order of convergence, contra harmonic mean, evaluation of function
MSC2020: 41A25, 41A58, 65H05