A Simple Hybrid Method for Finding the Root of Nonlinear Equations

Authors(1) :-Hassan Mohammad

In this paper, we proposed a simple modification of McDougall and Wotherspoon [11] method for approximating the root of univariate function. Our modification is based on the approximating the derivative in the corrector step of the proposed McDougall and Wotherspoon Newton like method using secant method. Numerical examples demonstrate the efficiency of the proposed method.

Authors and Affiliations

Hassan Mohammad
Department of Mathematical Sciences, Faculty of Sciences, Bayero University, Kano, Kano State, Nigeria

Secant method, Predictor- corrector, Nonlinear equations
Mathematics Subject Classification: 65K05, 65H05, 65D32, 34G20

  1. Dolan ED, Mor’e JJ. Benchmarking optimization software with performance profiles. Math Program Ser. A 2002; 91: 201-213.
  2. Ham YM , Chun C Sang-Gu Lee C. Some higher-order modification of Newton’s method for solving nonlinear equation. Journal of computation and Applied Mathematics 222:(2008); 477-486
  3. Homeier H. A modified Newtons method for root finding with cubic convergence. Journal of Computational and Applied Mathematics 157 : (2003);227 - 230
  4. Hewitt E, and Stromberg K. Real and abstract analysis springer-verlag. theorem 17.8 (1963).
  5. Jayakumar J. Generalised Simpson- Newton’s method for solving nonlinear equations with cubic convergence. IOSR journal of Mathematics 5: (2013); 58-61
  6. Kou J.The improvements of modified Newton’s method . Applied mathematics and computational 189:(2007); 602-609
  7. Kou J, Li Y andWang X. A modification of Newton’s method with third- order convergence. Journal Computation and Applied Mathematics 181 : (2006);1106 - 1111
  8. Kou J, Li Y and Wang X. Some modificatios of Newton’s method with fifth-order convergence. Journal of computational and applied Mathematics 209 : (2007);146 - 152
  9. Tiruneh AT, Ndelela WN, and Nkambule SJ. A Two- Point Newton Method Suitable For Nonconvergent Cases and with Super-Quadratic Convergence. Advances in Numerical Analysis. (2013);1-7.
  10. Mcdougall TJ, Jackett DR, Wright DGand Feistel R. Accurate and computationally efficient algoritms for potential temperature and density of seawater. J.Atmos ocean Technology. 23: (2006); 1709-1728
  11. McDougall TJ, Wotherspoon SJ. A simple modification of Newton’s method to achieve convergence of order  Journal of Applied and Mathematical letters 29: (2014); 20-25.
  12. Ozban AY. Some new variant of Newton’s method. Applied Mathematics letter 17 : (2004);677-682
  13. Scavo TR, Thou JB. On the geometry of halley’s method. American Mathematics Mounthy. 5: (1995); 417-426
  14. Soleymani F, Khattri K, Varani SK. Two new class optimal Jarratt-type fourth-order methods. Applied Mathematics letter 25:(2013); 847-853
  15. Wang P. A third -order family of Newton’s-like iteration method for solving nonlinear equations. Journal of Numerical Mathematics stochastic 3:(2011); 13-19.
  16. Weerakoon S, Fernando TG. A variant of Newton’s method with accelerated third-order convergence Applied mathematics letters 13 : (2000);87-93.

Publication Details

Published in : Volume 1 | Issue 4 | September-October 2015
Date of Publication : 2015-10-25
License:  This work is licensed under a Creative Commons Attribution 4.0 International License.
Page(s) : 80-83
Manuscript Number : IJSRST151420
Publisher : Technoscience Academy

Print ISSN : 2395-6011, Online ISSN : 2395-602X

Cite This Article :

Hassan Mohammad, " A Simple Hybrid Method for Finding the Root of Nonlinear Equations, International Journal of Scientific Research in Science and Technology(IJSRST), Print ISSN : 2395-6011, Online ISSN : 2395-602X, Volume 1, Issue 4, pp.80-83, September-October-2015. Available at doi : 10.32628/IJSRST151420
Journal URL : http://ijsrst.com/IJSRST151420

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