Higher-order families of multiple root finding methods suitable for non-convergent cases and their dynamics

In this paper, we present many new one-parameter families of classical Rall’s method (modified Newton’s method), Schröder’s method, Halley’s method and super-Halley method for the first time which will converge even though the guess is far away from the desired root or the derivative is small in the...

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Bibliographic Details
Main Authors: Ramandeep Behl, Vinay Kanwar, Young Ik Kim
Format: Article
Language:English
Published: Vilnius Gediminas Technical University 2019-06-01
Series:Mathematical Modelling and Analysis
Subjects:
Online Access:https://journals.vgtu.lt/index.php/MMA/article/view/5646
Description
Summary:In this paper, we present many new one-parameter families of classical Rall’s method (modified Newton’s method), Schröder’s method, Halley’s method and super-Halley method for the first time which will converge even though the guess is far away from the desired root or the derivative is small in the vicinity of the root and have the same error equations as those of their original methods respectively, for multiple roots. Further, we also propose an optimal family of iterative methods of fourth-order convergence and converging to a required root in a stable manner without divergence, oscillation or jumping problems. All the methods considered here are found to be more effective than the similar robust methods available in the literature. In their dynamical study, it has been observed that the proposed methods have equal or better stability and robustness as compared to the other methods.
ISSN:1392-6292
1648-3510