Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)Khayyam Journal of Mathematics2423-47884220180701Expanding the Applicability of Generalized High Convergence Order Methods for Solving Equations1671776336810.22034/kjm.2018.63368ENIoannis KArgyrosDepartment of Mathematical Sciences, Cameron University, Lawton, OK
73505, USA.0000-0002-9189-9298SanthoshGeorgeDepartment of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India-575 025.0000-0002-3530-5539Journal Article20180213 The local convergence analysis of iterative methods is important since it indicates the degree of difficulty for choosing initial points. In the present study we introduce generalized three step high order methods for solving nonlinear equations. The local convergence analysis is given using hypotheses only on the first derivative, which actually appears in the methods in contrast to earlier works using hypotheses on higher derivatives. This way we extend the applicability of these methods. The analysis includes computable radius of convergence as well as error bounds based on Lipschitz-type conditions, which is not given in earlier studies. Numerical examples conclude this study.http://www.kjm-math.org/article_63368_012c2c785e1430a9ff18422feb561db6.pdf