New Modification of Fixed Point Iterative Method for Solving Nonlinear Equations

Muhammad Saqib¹, Muhammad Iqbal², Shahzad Ahmed², Shahid Ali², Tariq Ismaeel³

¹Department of Mathematics, Govt. Degree College, Kharian, Pakistan.
²Department of Mathematics, Lahore Leads University, Lahore, Pakistan.
³Department of Mathematics, GC University, Lahore, Pakistan.

DOI: 10.4236/am.2015.611163                

Abstract

In this paper, we have modified fixed point method and have established two new iterative methods of order two and three. We have discussed their convergence analysis and comparison with some other existing iterative methods for solving nonlinear equations.

Keywords

Modifications, Fixed Point Method, Nonlinear Equations

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Abbasbandy, S. (2003) Improving Newton-Raphson Method for Nonlinear Equations by Modified Adomain Decomposition Method. Applied Mathematics and Computation, 145, 887-893. http://dx.doi.org/10.1016/S0096-3003(03)00282-0
[2]	Adomain, G. (1989) Nonlinear Atochastic Systems and Applications to Physics. Kluwer Academy Publishers, Dordrecht. http://dx.doi.org/10.1007/978-94-009-2569-4
[3]	Chun, C. (2005) Iterative Methods Improving Newton’s Method by Decomposition Method. Applied Mathematics and Computation, 50, 1595-1568. http://dx.doi.org/10.1016/j.camwa.2005.08.022
[4]	Noor, M.A. and Inayat, K. (2006) Three-Step Iterative Methods for Nonlinear Equations. Applied Mathematics and Computation, 183, 322-327.
[5]	Noor, M.A., Inayat, K. and Tauseef, M.D. (2006) An Iterative Method with Cubic Convergence for Nonlinear Equations. Applied Mathematics and Computation, 183, 1249-1255. http://dx.doi.org/10.1016/j.amc.2006.05.133
[6]	Babolian, E. and Biazar, J. (2002) On the Order of Convergence of Adomain Method. Applied Mathematics and Computation, 130, 383-387. http://dx.doi.org/10.1016/S0096-3003(01)00103-5
[7]	Kang, S.M., et al. (2013) A New Second Order Iteration Method for Solving Nonlinear Equations. Handawi Publishing Company, Abstract and Applied Analysis, 2013, Article ID: 487062.