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.

New Memory-Updating Methods in Two-Step Newton’s Variants for Solving Nonlinear Equations with High Efficiency Index

“…The drawbacks and limitations of the NM as just mentioned above induced a lot of studies that continue to the present and render some modifications of the Newton method, like the Adomian decomposition method [19], decomposition method [20], the arithmetic mean quadrature method [21], contra-harmonic mean and quadrature method [22], powermeans variants [23], modified homotopy perturbation method [24], generating function method [25], perturbation of Newton's method [26], and the variants of Bawazir's iterative methods [27].…”