Expanding the Applicability of Generalized High Convergence Order Methods for Solving Equations

Document Type: Original Article

Authors

1 Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA.

2 Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India-575 025.

Abstract

 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.

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