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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 3 | Issue 2 | Year 2012 | Article Id. IJMTT-V3I2P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V3I2P507

Improved Ujević method for finding zeros of linear and nonlinear equations


Anup Kumar Thander, Goutam Mandal
Abstract

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.

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

[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. 

Citation :

Anup Kumar Thander, Goutam Mandal, "Improved Ujević method for finding zeros of linear and nonlinear equations," International Journal of Mathematics Trends and Technology (IJMTT), vol. 3, no. 2, pp. 74-77, 2012. Crossref, https://doi.org/10.14445/22315373/IJMTT-V3I2P507

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