Visual Analysis of Mixed Algorithms with Newton and Abbasbandy Methods Using Periodic Parameters

Abstract

In this paper, we proposed two mixed algorithms of Newton’s and Abbasbandy’s methods using a known iteration scheme from fixed point theory in polynomiography. We numerically investigated some properties of the proposed algorithms using periodic sequence parameters instead of the constant parameters that are mostly used by many authors. Two pseudo-Newton algorithms were introduced based on the mixed iterations for the purpose of generating polynomiographs. The properties of the obtained polynomiographs were studied with respect to their graphics, turning effects and computation time. Moreover, some of these polynomiographs exhibited symmetrical properties when the degree of the polynomial was even.