The Optimal Order Newton’s Like Methods with Dynamics

Manoj Kumar Singh and Arvind K. Singh
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Manoj Kumar Singh: Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India
Arvind K. Singh: Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India

Mathematics, 2021, vol. 9, issue 5, 1-24

Abstract: In this paper, we have obtained three optimal order Newton’s like methods of order four, eight, and sixteen for solving nonlinear algebraic equations. The convergence analysis of all the optimal order methods is discussed separately. We have discussed the corresponding conjugacy maps for quadratic polynomials and also obtained the extraneous fixed points. We have considered several test functions to examine the convergence order and to explain the dynamics of our proposed methods. Theoretical results, numerical results, and fractal patterns are in support of the efficiency of the optimal order methods.

Keywords: Newton’s method; iteration function; order of convergence; efficiency index; Kung Traub conjecture; basin of attraction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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