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.
References
Amat, S. and Busquier, S. (2016). Advances in Iterative Methods for Nonlinear Equations, SEMA-SEMAI Springer series, Switzerland. DOI: https://doi.org/10.1007/978-3-319-39228-8
Jay, L. O. (2001). A note on Q-order of convergence, BIT Numerical Math., 41, 422–429. DOI: https://doi.org/10.1023/A:1021902825707
Jarratt, P. (1966). Some fourth-order multipoint iterative methods for solving equations, Math. Comput., vol 20, 434-437. DOI: https://doi.org/10.1090/S0025-5718-66-99924-8
Ogbereyivwe, O. and Izevbizua, O. (2023). A three param eter class of power series based iterative method for approximation of nonlinear equations. Iranian J. of Numerical Analysis and Optimization, vol 13, no. 2, pp.157-169.
Ogbereyivwe, O and Ojo-Orobosa, V. (2021). Families of means-based modified Newton's method for solving nonlinear models, Punjab University J. of Mathematics, vol. 53, no. 11, pp. 779-791. https://doi:org/10.52280/pujm.2021.531102. DOI: https://doi.org/10.52280/pujm.2021.531102
Petkovic, M., Neta, B., Petkovic, L. and Dzunic, J. (2013). Multipoint Methods for Solving Nonlinear Equations, Elsevier, Amsterdam, Netherlands.
Traub, J. F. (1964), Iterative methods for the solution of equations, Prentice-Hall, New Jersey.
Weerakoon, S. and Fernando, T. G. I. (2000). A variant of Newton’s method with third-order convergence, App. Math. Lett., vol. 13, no 1, pp. 87-93 DOI: https://doi.org/10.1016/S0893-9659(00)00100-2
Copyright (c) 2023 FUDMA JOURNAL OF SCIENCES
This work is licensed under a Creative Commons Attribution 4.0 International License.
FUDMA Journal of Sciences
