Improved Ujević method for finding zeros of linear and nonlinear equations

International Journal of Mathematical Trends and Technology (IJMTT)          
© 2012 by IJMTT Journal
Volume-3 Issue-2                           
Year of Publication : 2012
Authors : Anup Kumar Thander, Goutam Mandal


Anup Kumar Thander, Goutam Mandal "Improved Ujević method for finding zeros of linear and nonlinear equations"International Journal of Mathematical Trends and Technology (IJMTT),V3(2):74-77.June 2012. Published by Seventh Sense Research Group.

In this paper, we suggest a new predictor- corrector method for solving nonlinear equations by combining Halley’s method and Ujević method. The method is verified on a number of test examples and numerical results show that the proposed method is very effective with respect to Ujević method and Newton’s method for finding zeros of nonlinear equations.


[1]C.T. Kelly, Iterative Methods for Linear and Nonlinear Equations, SIAM, Philadelphia, PA, 1995.
[2]J. Naghipoor, S. A. Ahmadian and Ali R. Soheili, An Improved Regula Falsi Method for Finding Simple Zeros of Nonlinear Equations, Applied Mathematical Sciences, Vol. 2, no-8, pp.381 – 386, 2008.
[3]M. Aslam Noor, F. Ahmad, Numerical comparison of iterative methods for solving nonlinear equations,J.Appl.Math.Comput.,180, pp. 167-172, 2006.
[4]M. Aslam Noor, F. Ahmad, Sh. Javeed, Two-step iterative methods for nonlinear equations, J. Appl. Math. Computation. 181, pp. 1068- 1075, 2006.
[5]M. Frontini , E. Sormani, Third-order methods from quadrature formulae for solving systems of nonlinear equations, Applied Mathematics and Computation, 149, pp. 771–782, 2004 Nenad Ujević, A method for solving nonlinear equations,
[6]Appl. Math And Computation. 174, pp. 1416-1426, 2006.
[7]E. Babolian, J. Biazar, Solution of nonlinear equations by adomian decomposition method, Appl. Math. Comput. 132, pp. 167–172, 2002.
[8]K. Karthikeyan1 and V. M. Chandrasekaran, Few Numerical Algorithms for Minimization Unconstrained Non Linear Functions, Int. J. Pure Appl. Sci. Technol., 8(1), pp. 38-46, 2012.
[9]Tetsuro Yamamoto, Historical developments in convergence analysis for Newton's and Newton-like methods, Journal of Computational and Applied Mathematics 124, pp. 1-23, 2000.
[10]M.M. Hosseini, A Note on One-step Iteration Methods for Solving Nonlinear Equations, World Applied Sciences, 7, pp. 90-95, 2009. .

Halley’s method, Ujević method, Numerical examples, Nonlinear equations, Newton’s method