MULTI-STEP HIGH CONVERGENCE ORDER METHODS FOR SOLVING EQUATIONS

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 multi-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 Lipschitztype conditions not given in earlier studies. Numerical examples conclude this study. © 2021, Bulgarian Academy of Sciences, Institute of Mathematics and Informatics. All rights reserved.