Comparison of Some Iterative Methods of Solving Nonlinear Equations
International Journal of Theoretical and Applied Mathematics
Volume 4, Issue 2, April 2018, Pages: 22-28
Received: Dec. 23, 2017;
Accepted: May 15, 2018;
Published: Jul. 26, 2018
Views 973 Downloads 152
Okorie Charity Ebelechukwu, Department of Mathematics and Statistics, Faculty of Pure and Applied Sciences, Federal University, Wukari, Nigeria
Ben Obakpo Johnson, Department of Mathematics and Statistics, Faculty of Pure and Applied Sciences, Federal University, Wukari, Nigeria
Ali Inalegwu Michael, Department of Mathematics and Statistics, Faculty of Pure and Applied Sciences, Federal University, Wukari, Nigeria
Akuji Terhemba Fidelis, Department of Mathematics and Statistics, Faculty of Pure and Applied Sciences, Federal University, Wukari, Nigeria
Follow on us
This work focuses on nonlinear equation (x) = 0, it is noted that no or little attention is given to nonlinear equations. The purpose of this work is to determine the best method of solving nonlinear equations. The work outlined four methods of solving nonlinear equations. Unlike linear equations, most nonlinear equations cannot be solved in finite number of steps. Iterative methods are being used to solve nonlinear equations. The cost of solving nonlinear equations problems depend on both the cost per iteration and the number of iterations required. Derivations of each of the methods were obtained. An example was illustrated to show the results of all the four methods and the results were collected, tabulated and analyzed in terms of their errors and convergence respectively. The results were also presented in form of graphs. The implication is that the higher the rate of convergence determines how fast it will get to the approximate root or solution of the equation. Thus, it was recommended that the Newton’s method is the best method of solving the nonlinear equation f(x) = 0 containing one variable because of its high rate of convergence.
Nonlinear, Iterative Methods, Convergence, Variable
To cite this article
Okorie Charity Ebelechukwu,
Ben Obakpo Johnson,
Ali Inalegwu Michael,
Akuji Terhemba Fidelis,
Comparison of Some Iterative Methods of Solving Nonlinear Equations, International Journal of Theoretical and Applied Mathematics.
Vol. 4, No. 2,
2018, pp. 22-28.
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Aisha H.A; Fatima W.L; Waziri M.Y. (2014). International journal of computer application, vol 98business dictionary. (2016). www.Business dictionary.com. copyright 2001-2016, web finance, In
Dass H.K. and Rajnish Verma (2012).Higher Engineering Mathematics. Published by S. Chand and Company ltd (AN ISO 90012008 Company). Ram New Delhi- 110055.
Deborah Dent and Marcin Paaprzycki. (2000).Recent advances in solvers for nonlinear algebraic Equations. School of mathematical sciences, University of Southern Mississippi Hattiesburg.
Erwin Kreysig (2011). Advance Engineering Mathematics. Tenth edition. Published by John Wileyand sons, inc.
Free dictionary. (2011). American Heritage dictionary of the English language, fifth edition, copyright by Houghton Mifflin Harcourt publishing company.
Giberto E. Urroz. (2004).Solution of nonlinear equations. A paper document on solving nonlinearequation using Matlab.
John Rice (1969), Approximation of functions: Nonlinear and Multivariate Theory, Publisher; Addison–Wesley Publishing Company.
Kandasamy P. (2012). Numerical methods. Published by S. Chand and company ltd (AN ISO 9001; 2000 Company). Ram Nagar, new-Delhi – 110 055
Masoud Allame. (2001). A new method for solving nonlinear equations by Taylor’s Expansion. Conference paper, Islamic Azad University. Numerical analysis Encyclopedia Britannica online. .
Sara T.M. Suleiman. (2009).Solving Nonlinear equations using methods in the Halley class. Thesis for the degree of master of sciences.
Sona Taheri, Musa Mammadov (2012), Solving Systems of Nonlinear Equations using a Globally Convergent Optimization Algorithm Transaction on Evolutionary Algorithm and Nonlinear Optimization ISSN: 2229-8711 Online Publication, June 2012www.pcoglobal.com/gjto.htm