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

Authors

  • Oghovese Ogbereyivwe
    Delta State University of Science and Technology, Ozoro
  • Salisu Shehu Umar
    Department of Statistics, Auchi Polytechnic, Auchi.

Keywords:

Iterative scheme, Weerakoon and Fernando scheme, Power means, Nonlinear equations

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.

Dimensions

Amat, S. and Busquier, S. (2016). Advances in Iterative Methods for Nonlinear Equations, SEMA-SEMAI Springer series, Switzerland.

Jay, L. O. (2001). A note on Q-order of convergence, BIT Numerical Math., 41, 422–429.

Jarratt, P. (1966). Some fourth-order multipoint iterative methods for solving equations, Math. Comput., vol 20, 434-437.

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.

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

Published

31-12-2023

How to Cite

BEHIND WEERAKOON AND FERNANDO’S SCHEME: IS WEERAKOON AND FERNANDO SCHEME VERSION COMPUTATIONALLY BETTER THAN ITS POWER-MEANS VARIANTS?. (2023). FUDMA JOURNAL OF SCIENCES, 7(6), 368-371. https://doi.org/10.33003/fjs-2023-0706-2116

Issue

Vol. 7 No. 6 (2023): FUDMA Journal of Sciences - Vol. 7 No. 6

Section

Research Articles
Copyright & Licensing

FUDMA Journal of Sciences

How to Cite

BEHIND WEERAKOON AND FERNANDO’S SCHEME: IS WEERAKOON AND FERNANDO SCHEME VERSION COMPUTATIONALLY BETTER THAN ITS POWER-MEANS VARIANTS?. (2023). FUDMA JOURNAL OF SCIENCES, 7(6), 368-371. https://doi.org/10.33003/fjs-2023-0706-2116