New Twelfth Order J-Halley Method for Solving Nonlinear Equations
[1]
Farooq Ahmad, Mathematics Department, College of Science, Majmaah University, Alzulfi, Saudi Arabia.
[2]
Sajjad Hussain, Mathematics Department, College of Science, Majmaah University, Alzulfi, Saudi Arabia.
[3]
Sifat Hussain, Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan.
[4]
Arif Rafiq, Department of Mathematics, COMSATS Institute of Information Technology, Islamabad 44000, Pakistan.
In a paper, Noor and Noor [Predictor--corrector Halley method for nonlinear equations, Appl. Math. Comput., 188 (2) (2007) 1587--1591] have suggested and analyzed a predictor--corrector method Halley method for solving nonlinear equations. In this paper, we modified this method by using the finite difference scheme, which has a quantic convergence. We have compared this modified Halley method with some other iterative of fifth-orders convergence methods, which shows that this new method is a robust one. Several examples are given to illustrate the efficiency and the performance of this new method.
Halley Method, Jarratt Method, Iterative Methods, Convergence Order, Numerical Examples
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