Generating Optimal Eighth Order Methods for Computing Multiple Roots

• Published in: Symmetry (Basel) Vol. 12; no. 12; p. 1947
• Main Authors: Kumar, Deepak, Kumar, Sunil, Sharma, Janak Raj, d’Amore, Matteo
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-12-2020
• Subjects: Basins; Computing time; Convergence; Efficiency; Iterative methods; Methods; multiple roots; Neighborhoods; Newton method; nonlinear equations; Numerical analysis; Numerical methods; optimal convergence
• ISSN: 2073-8994; 2073-8994
• DOI: 10.3390/sym12121947

There are a few optimal eighth order methods in literature for computing multiple zeros of a nonlinear function. Therefore, in this work our main focus is on developing a new family of optimal eighth order iterative methods for multiple zeros. The applicability of proposed methods is demonstrated on some real life and academic problems that illustrate the efficient convergence behavior. It is shown that the newly developed schemes are able to compete with other methods in terms of numerical error, convergence and computational time. Stability is also demonstrated by means of a pictorial tool, namely, basins of attraction that have the fractal-like shapes along the borders through which basins are symmetric.