BEHIND WEERAKOON AND FERNANDO’S SCHEME: IS WEERAKOON AND FERNANDO SCHEME VERSION COMPUTATIONALLY BETTER THAN ITS POWER-MEANS VARIANTS?

Abstract

The Weerakoon and Fernando scheme for estimating the solution of nonlinear equations is a modification of the Newton iteration scheme (NIS) with better convergence order and efficiency. It was developed based on the composition of the NIS with a corrector iterative function that is based on the use of arithmetic mean. In this article, we put forward family of power-means variants of the Weerakoon and Fernando iterative scheme. The family is shown to have convergence order three. Numerical studies on the family enabled us to decide whether the classical Weerakoon and Fernando scheme version is computationally better than its power-means variants versions. From the numerical results, it is discovered that there are some highly efficient and competitive elements in the developed family of Weerakoon and Fernando scheme version.