Solving a Nonlinear Equation Using a New Two-Step Derivative Free Iterative Methods
Applied and Computational Mathematics
Volume 6, Issue 6, December 2017, Pages: 238-242
Received: Aug. 8, 2017;
Accepted: Sep. 26, 2017;
Published: Nov. 7, 2017
Views 1460 Downloads 172
Alyauma Hajjah, Department of Informatics Technical, (Sekolah Tinggi Ilmu Komputer) STIKOM Pelita Indonesia, Pekanbaru, Indonesia
In this paper, suggest anew two step iterative method for solving a nonlinear equation, which is derivative free by approximating a derivative in the iterative method by central difference with one parameter θ. The anew derivative free iterative method has a convergence of order four and computational cost the family requires three evaluations of functions per iteration. Numerical experiments show that the proposed a method is comparable to the existing method in terms of the number of iterations.
Solving a Nonlinear Equation Using a New Two-Step Derivative Free Iterative Methods, Applied and Computational Mathematics.
Vol. 6, No. 6,
2017, pp. 238-242.
Copyright © 2017 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.
K. E. Atkinson. Elementary Numerical Analysis, 2nd Ed. John Wiley, New York, 1993.
M. S. M. Bahgat, and M. A. Hafiz, 2014. Three-Step Iterative Method with eighteenth order convergence for solving nonlinear equations, International Journal of Pure and Applied Mathematics. Vol.93, No.1, 85-94.
W. Bi, H. Ren, and Q. Wu (2009). Three-step Iterative Methods with Eight-order Convergence for Solving Nonlinear Equations, Journal of Computation and Applied Mathmatics, 225, 105-112.
A. Cordero, J. L. Hueso, E. Martinez, and J. R. Torregrosa, 2011. Steffensen type methods for solving nonlinear equations, Journal of Computational and Applied Mathematics, doi: 10.1016/j.cam. 2010.08.043.
M. Dehghan and M. Hajarian. Some Derivative Free Quadratic and Cubic Convergence Iterative Formulas for Solving Nonlinear Equation, J. Comput. Appl. Math, 29 (2010), 19-31.
W. Gautschi, Numerical Analysis: an Introduction, Birkhauser, 1997.
A. Hajjah, M. Imran and M. D. H. Gamal. A Two-Step Iterative Methods for Solving Nonlinear Equation, J. Applied Mathematics Sciences, Vol.8, 2014, No.161, 8021-8027.
M. Imran, Agusni, A. Karma, S. Putra. Two Step Methods Without Employing Derivatives for Solving a Nonlinear Equation, Bulletin of Mathematics. Vol.04, 2012, No.01, 59-65.
R. Intan, M. Imran, and M. D. H. Gamal. A Three-step Derivative Free Iterative Method for Solving a Nonlinear Equation, J. Applied Mathematics Scinces, Vol. 8, 2014, No. 89, 4425 – 4431.
J. P. Jaiswal. A New Third-Order Derivative Free Method for Solving Equations, Univ. J. Appl. Math. Comput, 184 (2006), 471-475.
K. Jisheng, L. Yetian and W. Xiuhui. A Composite Fourth-Order Iterative Method for Solving, Appl. Math. 1 (2013), 131-135.
R. F. King. A Family of Fourth Order Methods for Nonlinear Equations, SIAM J. Numer. Anal. 10 (1973), 876-879.
J. H. Mathews. Numerical Method for Mathematical Science and Engineer, Prentice-Hall International, Upper Saddle River, NJ, 1987.
D. Nerinckx and D. Haegenans. A Comparison of Non-linear Equation Solver, J. Comput. Appl. Math. 2 (1976), 145148.
J. R. Rice. A set of 74 test functions non-linear equation solvers, Report Purdue University CSD TR 34 (1969).
R. Wait. The Numerical Solution of Algebraic Equation, Jhon Wiley and Sons, New York, 1979.
S. Weerakon, T. G. I. Fernando, A variant of Newton’s method with accelerated third-order convergence. Appl. Math. Lett. 13(2000) 87-93.