Visual analysis of mixed algorithms with Newton and Abbasbandy methods using periodic parameters

Khan, Safeer Hussain, Jolaoso, Lateef Olakunle and Aphane, Maggie (2022) Visual analysis of mixed algorithms with Newton and Abbasbandy methods using periodic parameters. Symmetry, 14 (12), [2484]. (doi:10.3390/sym14122484).

Record type: Article

Abstract

In this paper, we proposed two mixed algorithms of Newton’s and Abbasbandy’s methods using a known iteration scheme from fixed point theory in polynomiography. We numerically investigated some properties of the proposed algorithms using periodic sequence parameters instead of the constant parameters that are mostly used by many authors. Two pseudo-Newton algorithms were introduced based on the mixed iterations for the purpose of generating polynomiographs. The properties of the obtained polynomiographs were studied with respect to their graphics, turning effects and computation time. Moreover, some of these polynomiographs exhibited symmetrical properties when the degree of the polynomial was even.

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Accepted/In Press date: 15 November 2022

e-pub ahead of print date: 21 November 2022

Additional Information: Funding Information: This research was funded by the Sefako Makgatho Health Sciences University Postdoctoral research fund, and the APC was funded by the Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Pretoria, South Africa.

Keywords: Abbasbandy’s method, mixed algorithms, Newton’s method, periodic parameters, polynomiographs, sequence parameters