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 functionMSC2020: 41A25, 41A58, 65H05