Visual Analysis of Mixed Algorithms with Newton and Abbasbandy Methods Using Periodic Parameters

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...

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Bibliographic Details
Published in:Symmetry (Basel) 2022-12, Vol.14 (12), p.2484
Main Authors: Khan, Safeer Hussain, Jolaoso, Lateef Olakunle, Aphane, Maggie
Format: Article
Language:English
Subjects:
Abbasbandy’s method
Algorithms
Analysis
Approximation
Basins
Fixed points (mathematics)
Fractals
Hypotheses
Iterative methods
Methods
mixed algorithms
Newton’s method
Parameters
periodic parameters
Polynomials
polynomiographs
sequence parameters
Technology application
Textile design
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Summary: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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14122484