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New Ninth Order J-Halley Method for Solving Nonlinear Equations
Punjab Higher Education Department, Principal, Govt. Degree College Darya Khan, Bhakkar, Pakistan
Centre for Advanced Studies in Pure and Applied Mathematics, B. Z. Uni., Multan, Pakistan
Centre for Advanced Studies in Pure and Applied Mathematics, B. Z. Uni., Multan, Pakistan
Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan
- 1 Punjab Higher Education Department, Principal, Govt. Degree College Darya Khan, Bhakkar, Pakistan
- 2 Centre for Advanced Studies in Pure and Applied Mathematics, B. Z. Uni., Multan, Pakistan
- 3 Centre for Advanced Studies in Pure and Applied Mathematics, B. Z. Uni., Multan, Pakistan
- 4 Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan
Applied Mathematics·Volume 04 (2013)·Pages 1709–1713·Published 8 November 2013·DOI10.4236/am.2013.412233
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Abstract
In the paper [1] , authors ha ve suggested and analyzed a predictor-corrector Halley method for solving nonlinear equa tions. In this paper, we modified this method by using the finite difference scheme, which ha d a quantic convergence. We have compared this modified Halley method with some other iterative methods of ninth order, which shows that this new proposed method is a robust one. Some examples are given to illustrate the efficiency and the performance of this new method.
KeywordsHalley MethodJarratt MethodIterative MethodsConvergence OrderNumerical Examples
- K. I. Noor and M. Aslam Noor, “Predictor-Corrector Halley Method for Nonlinear Equations,” Applied Mathematics and Computation, Vol. 188, No. 2, 2007, pp. 15871591. http://dx.doi.org/10.1016/j.amc.2006.11.023
- J. Kou and Y. T. Li, “The Improvements of ChebyshevHalley Methods with Fifth-Order Convergence,” Applied Mathematics and Computation, Vol. 188, No. 1, 2007, pp. 143-147. http://dx.doi.org/10.1016/j.amc.2006.09.097
- J. Kou, Y. T. Li and X. H. Wang, “A Family of FifthOrder Iterations Composed of Newton and Third-Order Methods,” Applied Mathematics and Computation, Vol. 186, No. 2, 2007, pp. 1258-1262. http://dx.doi.org/10.1016/j.amc.2006.07.150
- J. Kou and Y. Li, “An Improvement of the Jarrat Method,” Applied Mathematics and Computation, Vol. 189, No. 2, 2007, pp. 1816-1821. http://dx.doi.org/10.1016/j.amc.2006.12.062
- Z. Y. Hu, L. Guocai and L. Tian, “An Iterative Method with Ninth-Order Convergence for Solving Nonlinear Equations,” International Journal of Contemporary Mathematical Sciences, Vol. 6, No. 1, 2011, pp. 17-23.
- M. A. Noor and K. I. Noor, “Fifth-Order Iterative Methods for Solving Nonlinear Equations,” Applied Mathematics and Computation, Vol. 188, No. 1, 2007, pp. 406410. http://dx.doi.org/10.1016/j.amc.2006.10.007
- S. Amat, S. Busquier and J. M. Gutierrez, “Geometric Construction of Iterative Functions to Solve Nonlinear Equations,” Journal of Computational and Applied Mathematics, Vol. 157, No. 1, 2003, pp. 197-205. http://dx.doi.org/10.1016/S0377-0427(03)00420-5
- I. K. Argyros, D. Chen and Q. Qian, “The Jarratt Method in Banach Space Setting,” Journal of Computational and Applied Mathematics, Vol. 51, No. 1, 1994, pp. 103-106. http://dx.doi.org/10.1016/0377-0427(94)90093-0
- J. A. Ezquerro and M. A. Hernandez, “A Uniparametric Halley-Type Iteration with Free Second Derivative,” International Journal of Pure and Applied Mathematics, Vol. 6, No. 1, 2003, pp. 103-114.
- J. A. Ezquerro and M. A. Hernandez, “On Halley-Type Iterations with Free Second Derivative,” Journal of Computational and Applied Mathematics, Vol. 170, No. 2, 2004, pp. 455-459. http://dx.doi.org/10.1016/j.cam.2004.02.020
- E. Halley, “A New Exact and Easy Method for Finding the Roots of Equations Generally and without any Previous Reduction,” Philosophical Transactions of the Royal Society of London, Vol. 18, 1964, pp. 136-147. http://dx.doi.org/10.1098/rstl.1694.0029