An improved optimal eighth-order iterative scheme with its dynamical behaviour

Abstract

In this paper, we have designed an improvement of the very recently constructed sixth-order iterative method without memory by using the weight function technique. Our scheme is optimal because it reaches the highest possible order using four function evaluations. Ten nonlinear test functions have been taken into account to check the reliability of the proposed scheme. Finally, dynamics of the proposed methods with some existing methods, illustrated in the paper.