Some New Three Step Iterative Methods for Solving Nonlinear Equation Using Steffensen’s and Halley Method
Najmuddin Ahmad *
Department of Mathematics, Integral University, Lucknow, Uttar Pradesh, India.
Vimal Pratap Singh
Department of Mathematics, Integral University, Lucknow, Uttar Pradesh, India.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we introduce the comparative study of new three step iterative methods for finding the zeros of the nonlinear equation f(x) = 0. The new method based on the Steffensen’s method and Halley method with using predictor – corrector technique. It is established that the new method (NTSM-1) has convergence order sixth and second new method (NTSM-2) has convergence order seventh. Numerical tests show that the new methods is comparable with the well known existing methods and gives better results.
Keywords: Non linear equations, iterative methods, three step, convergence analysis, Halley method, Steffensen’s method